Identification of a long lived β decaying isomer in ^{150}Pm
A. Saha, T. Bhattacharjee, D. Banerjee, S. S. Alam, Deepak Pandit, M. Saha Sarkar, S. Sarkar, P. Das, Soumik Bhattacharya, R. Guin, S. K. Das, S. R. Banerjee
IIdentification of a long lived β decaying isomer in Pm A. Saha,
1, 2
T. Bhattacharjee,
1, 2, ∗ D. Banerjee, S. S. Alam,
1, 2
Deepak Pandit, M. Saha Sarkar, S. Sarkar, P. Das,
1, 2
Soumik Bhattacharya,
1, 2
R. Guin, S. K. Das, and S. R. Banerjee
1, 2 Variable Energy Cyclotron Centre, Kolkata - 700 064, India Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai - 400 094, India RCD-BARC, Variable Energy Cyclotron Centre, Kolkata - 700 064, India Saha Institute of Nuclear Physics, Kolkata - 700 064, India Indian Institute of Engineering Science and Technology, Shibpur, West Bengal - 711 103, India (Dated: October 15, 2018)The decay of odd-odd
Pm has been studied by populating the nucleus with the
Nd(p,n)
Pm reaction at E beam = 8.0 MeV using 97% enriched
Nd target. The presenceof an isomeric state with β decay half life of 2.2(1) h could be identified in Pm by following thehalf lives of the observed γ transitions. The decay of the isomer to the excited levels of Sm hasbeen confirmed by observing the γ − γ coincidence with the VENUS array of six Compton sup-pressed Clover HPGe detectors. The β decay end-point energies corresponding to the decay fromthe g Pm and m Pm have been measured using a β − γ coincidence setup of two thin windowPlanar HPGe detectors and four Clover HPGe detectors of the VENUS array. The systematicsof the similar isomeric states in neighboring nuclei has been studied to understand the underlyingstructure of these states. Shell model calculation has been performed by using OXBASH code whichindicates the presence of a 5 − isomeric state at very low excitation in the nucleus. The calculationalso suggests hindered electromagnetic decay of this isomer and supports the possibility of its β decay to the excited levels of Sm.
PACS numbers: 23.20.Lv; 23.40.s; 21.10.Tg; 21.60.CsKeywords: Nuclear Structure; Decay γ spectroscopy; β decay; HPGe detector; Shell Model Calculation. I. INTRODUCTION
The odd-odd
Pm nucleus lies in the transitional re-gion between N = 88 and N = 90 with three proton holescompared to the subshell closure of Z = 64. The groundstate shape transition as a function of neutron number,associated with the softness of the collective potential,has been observed in this region and remained a topicof both experimental and theoretical interest [1–6]. Sim-ilar shape transition is also indicated in case of odd-A Pmnuclei from the results obtained using neutron proton In-teracting Boson Fermion Model calculation (IBFM) [7].In this work, it has been observed that the experimentalenergy spectra of
Pm and
Pm nuclei could be re-produced by coupling the odd proton with a vibrationalcore whereas a rotational core was required for
Pmand
Pm.In the odd-odd nuclei of this mass region, several longlived isomeric states are known and predicted [8]. Thesystematics of the low lying states in the odd-odd nucleiaround
Pm also reveal that the said isomers are ob-served in many of these nuclei [9–13], as shown in Fig. 1and 2. However, no such isomeric state is known till datein case of N = 89 Pm nucleus [14]. These isomers ob-served in the deformed odd-odd nuclei around Pm aremostly understood on the basis of Gallagher Moszkowski(GM) rule [15] for coupling of angular momentum based ∗ Corresponding author; Electronic address: [email protected] on the Nilsson configurations of the neighboring odd Zand odd N nuclei. However, this type of calculation isnot appropriate for the nuclei having very low deforma-tion where the shell model calculations might be the rightchoice. Also, the existing knowledge about the structureand the associated configurations for the low lying levelsin the neighboring nuclei is very scanty [16–19]. Hence,the systematic understanding of these isomers is chal-lenging in the context of choosing the appropriate modelbased calculation and also the available information inthe neighboring nuclei. This might be the most probablereason for the fact that the nucleonic configurations ofthe two known isomers in
Pm are unassigned till date.Most of the long lived isomeric states in the odd-oddnuclei around
Pm, having half lives greater or similarto that of the ground state, undergo β decay and havevery low IT decay probability to the ground state. Thepresence of these isomers have important effect on the β decay branching of the slow neutron capture process(s-process) of nucleo-synthesis. The evidence of the exis-tence of such branch point around Pm and its effect onthe s-process path and s-process neutron density is dis-cussed in the work of Lesko et al. [21]. Hence, the char-acterization of these isomers close to the branch point isvery important also to understand the synthesis of heavynuclei around the β stability line.The experimental information on the low lying excitedstates of Pm is limited to a preliminary work based onin-beam spectroscopy using (p,n γ ), ( He,d) and (p,t) re-actions [22]. However, the isomers with τ ∼ sec or more a r X i v : . [ nu c l - e x ] J un FIG. 1: The systematics of the isomeric states in Z = 61 isotopes neighboring to
Pm. The data is taken from ENSDFdatabase [20]. The J π of the ground state in Pm is suggested to be 2 − of [22].FIG. 2: The systematics of the isomeric states in N = 89 isotones neighboring to Pm. The data is taken from ENSDFdatabase [20]. The J π of the ground state of Pm is suggested to be 2 − in [22]. can not be detected in an in-beam experiment and hence,the decay measurement becomes very crucial. Identifica-tion of these β decaying isomers can be done by studyingthe decay curves for the observed γ rays of the daughterand the γ − γ coincidence measurements involving thesedecay γ transitions. Measurement of β decay end-pointenergies, when measured in coincidence with the daugh-ter γ transitions, is also important in order to assign theexcitation energy of the isomeric level, especially in ab-sence of any isomeric transition decaying to the groundstate of the parent. The measurement of intensities of the β -feeding gives the information on the logft values whichin turn can be used to guess the spin of the isomeric leveland the spin of the excited states of the daughter. Onlya single decay spectroscopy work of Pm by Barret etal., [23] exists in literature in which the γ rays were de-tected with a Ge(Li) detector and the coincidence infor-mation was obtained by using a well type Ge(Li) detectorwith the help of summing technique. In this work, the de-cay curves were not studied for the observed γ transitionswhich can be helpful in verifying their placement in thedecay scheme of 2.7 h Pm ground state. This mightbe the reason for which the identification of any isomericstate in
Pm was not possible in this work. Hence, thedecay spectroscopy of
Pm must be performed with thecareful measurement of decay half lives followed by theobserved transitions and the γ − γ coincidence to identifythe presence of any long lived isomer in Pm. Also, no measurement exists for the β decay end point energies inthe decay of Pm to the excited states of
Sm [14].In the present work, decay spectroscopy of
Pm hasbeen carried out, on the basis of the study of systematcs,to search for the existence of any long-lived isomeric statein this nucleus. The measured half lives followed by theobserved transitions and their γ − γ coincidence relation-ship indicate the presence of a 2.2(1)h isomeric state inodd-odd Pm for the first time. The β decay logft val-ues have been obtained to guess the spin parity of thelevels in Sm daughter nucleus which are fed by theisomer in
Pm. The β end-point energies correspond-ing to several decay branches of g Pm → Sm decaywere measured for the first time by using the β − γ co-incidence technique [24]. The energy of the isomericstate has been determined from the measurement of β end-point energies corresponding to the isomeric decay.A systematic study of all such isomers existing around Pm has been carried out. Shell Model calculation hasbeen performed by using OXBASH code [25] that showsthe presence of a 5 − isomer in the level scheme of Pm.The calculation also indicates the possibility of β decayfrom this isomer with a highly hindered electromagnetictransition probability. II. EXPERIMENTAL DETAILS
The excited states of
Pm was populated by the
Nd (p, n)
Pm reaction using 8.0 MeV proton beamsprovided by K = 130 AVF cyclotron at Variable EnergyCyclotron Centre (VECC), Kolkata. The beam energywas chosen from the measured excitation function forthe p +
Nd reaction [26] so as to have maximumcross section for the (p,n) channel. The
Nd targetwas prepared by electro-deposition technique, startingfrom commercially available 97.65% enriched powderedoxide sample (Nd O ), on a 0.3 mil thick Aluminium(Al) foil. The isotopic impurities in the target materialconsisted of 0.50% Nd, 0.31%
Nd, 0.68%
Nd,0.23%
Nd, 0.47%
Nd and 0.26%
Nd, as per thedata sheet provided by the supplier. The thickness ofthe targets used in the experiment was ∼ µ g/cm .Several targets were irradiated following the stacked foiltechnique [26]. The irradiated targets were subsequentlycounted with different configurations of Ge detectors asper the requirement of the decay spectroscopy measure-ments as discussed below.In the present work, the decay γ transitions have beendetected using the VENUS (VECC Array for NUclearSpectroscopy) array of six Compton suppressed CloverHPGe (High Purity Ge) detectors [27] which were placedat the angles of 30 ◦ , 90 ◦ , 180 ◦ , 260 ◦ and 310 ◦ w.r.t one ofthe detectors taken as a reference of 0 ◦ and at a distanceof 18 cm from the target. In order to measure the decayhalf lives, the γ decay was followed in singles mode overa period of ∼
10h where each counting was continued fora duration of 10 minutes. It was also ensured that thedetector dead time is kept below 5% during counting. Inthe γ − γ coincidence measurement, conventional two foldcoincidence logic was used for gathering the data with theVENUS array.The β decay endpoint energies were determined from β − γ coincidence measurement [24] by using two LowEnergy Photon Spectrometer (LEPS), having 300 µ m Bewindow, in conjunction with four Clovers of the VENUSarray. During this measurement, only the bare target hasbeen used by placing it in such a way that the irradiatedtarget material faces the LEPS detectors and ensures theefficient emission of β particles from the target material.Each LEPS detector is made up of a planar HPGe crystalwhich is electrically separated in four segments providingfour individual signals. Data were gathered in two differ-ent modes of (i) γ − ( β + γ ) and (ii) γ − γ establishingtwo fold coincidence among the set of four Clover detec-tors and the eight segments of the two LEPS detectors,respectively. In this measurement, the γ − γ coincidencedata was taken by placing Al blocks of 10 mm thicknessin between the detector and the target in order to com-pletely stop the β particles from reaching the detectorsas and when required. For the β − γ measurements, thetarget to detector distance was kept as 10.5 cm.The pulse processing for the present work was per-formed by using sixteen channel Mesytec high resolution Shaper and Amplifier module and VME DAQ systemLAMPS [28] with the 32 bit Mesytec ADC (MADC-32).All the decay measurements have been carried out aftera cooling time of ∼ Eu and
Ba sources of known activ-ity. All the data were gathered in zero suppressed LISTmode and the offline analysis were performed using theLAMPS and RADWARE [29] analysis packages.
III. DATA ANALYSIS AND RESULTS
The data analysis was performed in order to (i) de-termine the decay half lives followed by the observed γ transitions, (ii) study the γ − γ coincidences, (iii) mea-surement of γ intensities & calculation of logft values and(iii) determine the β decay end point energies. The de-tails of data analysis and the results obtained from thepresent work have been discussed in the following sub-sections. A. Measurement of Decay Half Lives
The γ transitions obtained from the singles modecounting are shown in Fig. 3 and the decay curves ex-hibited by all of them were studied in order to iden-tify the origin of each transition. This was performedby using the standard techniques where the backgroundsubtracted areas of a particular full energy peak werestudied as a function of time. Most of the observed tran-sitions belong to the level scheme of Sm, the β − decaydaughter nucleus of Pm which is produced via (p,n)reaction. The 286 keV γ transition which is known inthe level scheme of Sm, produced via β decay of the(p,2n) reaction channel, was also found to be present inthe spectrum. No γ transition has been identified whichare originated from other Nd isotopes present in the en-riched Nd target. Three new transitions were foundin the singles data and the placement of these transi-tions could be confirmed in the level scheme of
Smby following decay half lives and γ − γ coincidence anal-ysis. However, some of the transitions are observed tobe decaying with much longer half lives and these wereidentified to be originating from either the impurities inthe Al backing foil or from background.Excluding the transitions which were identified as com-ing from sources other than Sm, two main groups oftransitions were observed. One of these two groups isobserved to decay with half life similar to the half lifefor
Pm ground state ( ∼ ∼ Pm ground state. Fig. 4 shows therepresentative experimental decay curves for some of thetransitions belonging to the said two groups.
FIG. 3: (Color Online) The singles spectrum showing all thetransitions observed from the decay measurement. The tran-sitions with no marking (in black) are already placed in thelevel scheme of
Sm from the decay of
Pm. The tran-sitions marked with
Sm [14], but not placed in the level scheme in the earlierexperiments. The transitions marked with % (in red) are thenew transitions observed for the first time in the present work.The 286 keV transition, marked with $ (in pink), is identifiedto be arising from the decay of
Pm ( τ / = 53.08(5) h).The (violet) transitions marked with @ follow longer half livesand have been identified to be coming from background or thecontaminations in the Al backing foil.FIG. 4: (Color Online) The decay curves are shown for twogroups of transitions, corresponding to two different half lives.The data points could be fitted with straight lines havingdifferent slopes and are shown. Different symbols correspondto different transition energies which are indicated along withthe obtained half life values. FIG. 5: (Color Online) The half life values obtained by fol-lowing the yields of the observed transitions are shown as afunction of energy. The data points corresponding to differenthalf lives are indicated with different colours and symbols. The observation has been summarised by showingFig. 5 where the half life values followed by all the ob-served transitions of
Sm have been plotted as a func-tion of energy. In the present work, six transitions, viz.,1810, 1893, 2174, 2384, 2624 and 3038 keV transitionshave been observed to exhibit decay curves with half lives ∼ Sm [14]. However, the 1893 and 2624keV transitions were not placed in the level scheme of
Sm, although these two transitions were known fromthe decay of
Pm [23]. The 2384 keV transition is ob-served for the first time in the present work but followshalf life different than the ground state of
Pm. Inthe present work, all these six transitions were confirmedto be present in
Sm from the analysis of γ − γ coinci-dences as described in the following subsection. From theobservation of two different half lives followed by the γ transitions belonging to the level scheme of Sm, whichcan only be produced from the β decay of Pm, thepresent work proposes the existence of a β decaying iso-mer in the level scheme of Pm. The half life for theproposed β decaying isomer in Pm was determinedfrom the weighted average value of the half lives followedby these six transitions and it comes out to be 2.2(1) h.
B. Measurement of γ − γ coincidences The γ − γ coincidence analysis was performed only forthose transitions which are relevant for the developmentof the decay scheme of the observed isomer and the samehas been described below. The γ − γ coincidence informa- FIG. 6: The 334 keV (2 + → + transition in Sm) gatedspectra showing the transitions belonging to
Sm nucleus.The transitions showing half lives ∼ tion regarding all other transitions belonging to the decayscheme of g Pm and observed in the present experimentmay be reported in future. Out of the six transitions fol-lowing half lives ∼ Sm. Theremaining five transitions, viz., 1810, 1893, 2174, 2384and 2624 keV, could be found in the 334 keV gated spec-trum, as shown in Fig. 6. The gated spectra for thesefive transitions, viz., 1810, 1893, 2174, 2384 and 2624keV, have been shown in Fig. 7 and Fig. 8. The threehigher energy transitions, viz., 2174, 2384 and 2624 keV,are found to be in coincidence only with the 334 keV(2 + → + ) transition of Sm. The lower energy transitions,viz., 1810 and 1893 keV, display coincidence with otherhigher lying transitions of
Sm as well.The 1893 keV transition was known in the ENSDFdatabase but was not assigned to the level scheme of
Sm [14]. In the present work, the transition has beenconfirmed to be present in the level scheme of
Smfrom the γ − γ coincidence analysis, as shown in Fig. 8.From the coincidence data, the energy of the excitedlevel comes out to be 2939 keV that de-excites by the1893 keV transition. A 2937 keV level is known from the(n, γ ), (p,t) and (d,p) reactions, however, no γ transitionwas known to decay from this level. Also, the energy ofthis level is uncertain by 20 keV as reported in ENSDFdatabase [14]. The 2939 keV level proposed in the presentwork could be same as the 2937 keV level reported fromearlier works.The 2624 keV transition is known from the decay of Pm [23] and in the present work, it could be placedin the level scheme of
Sm from the γ − γ coincidenceanalysis, as shown in Fig. 7. It is found to be decay- FIG. 7: The gated spectra for three higher energy transitionsshowing half lives ∼ (cid:63) . ing from a 2958 keV excited state in Sm as per theobserved coincidence with the 334 keV transition. This2958 keV level has been assigned in the level scheme of
Sm for the first time in the present work.The 1810 keV transition is known to be decaying fromthe 2550.6 keV level, as per the β decay work [23]. The γ − γ coincidence analysis, as shown in Fig. 8, confirmsthat the 1810 keV transition is in coincidence with 334and 407 keV transitions. The 2550.6 keV level also de-cays via two more transitions, viz., 2550.5 and 2216.5keV. However, these two transitions were found to followhalf lives close to the half life of the Pm ground stateand, thus, can not be originated from the proposed iso-meric level. Moreover, an accurate energy measurementof the involved transitions (1809.9, 334.3 and 406.8 keV)suggests that the 1810 keV γ ray is decaying from a 2551keV level. The similar energy measurement for the ear-lier known 2550.5 and 2216.5 keV transitions yields thevalues of 2549.5 keV and 2216.1 keV respectively. Hence,it is proposed that there might be two close lying levelsexisting in Sm, one at 2550 keV, decaying the 2549.5and 2216.1 keV transitions and the other at 2551 keV de-exciting via 1810 keV transition. In the present work, thelatter level is proposed to be fed by the ∼ Pm.The 2174 keV transition is decaying from the 2507.3keV level from which four more transitions of energy2507, 1437, 1341 and 848 keV are known to be decayingout. In the present work, the 848 keV has been found tofollow longer half life and thus, confirmed to be originat-ing from contamination in the Al backing. The 1341 keVtransition was not observed in the present work. Thetwo remaining transitions of energy 2507 and 1437 keVshow decay curves with half life close to the half life ofthe ground state of
Pm. In the ENSDF database of
Sm, two levels are known at around 2507 keV. Oneof them is 2507.27 keV,(1 − , 2 + ) level assigned from the β decay work and the other is 2507.5 keV, 3 + , 4 + levelwhich was observed from the (n, γ ) reaction. It is, thus,conjectured that the 2507.5 keV level, having higher spinvalue (3 + , 4 + ), is fed by the 2.2 h isomer in Pm anddecays by the 2174 keV γ transition. This was based onthe observation of difference in half life followed by the2174 keV transition compared to the other two transi-tions, viz., 2507 and 1437 keV, decaying from the 2507.3keV level and the γ − γ coincidence information, as ob-tained from Fig. 7.The 2384 keV transition is observed for the first timein the present work and shows coincidence with the 334keV transition (cf. Fig. 7). Following its coincidence re-lationships, this γ ray has been placed as decaying fromthe 2718 keV level. One 2715(4) keV, 3 − level is knownin Sm from the (p,p (cid:48) ) and (d,d (cid:48) ) reactions [14]. How-ever, no γ transition is known to be decaying from thislevel. In the present work, it is proposed that the newlyobserved 2718 keV level could be same as the 2715(4)keV level reported already in ENSDF database.The 3038 keV level is also known in the level scheme of Sm from which the 3038 keV transition is known to bedecaying directly to the ground state of
Sm. As men-tioned above, this 3038 keV transition has been observedin the present work and follows a half life ∼ ∼ β decayingisomeric state in Pm is developed and has been shownin Fig. 9. A spin parity of 5 − is predicted for this isomerfrom the shell model calculation (cf. Section V) and thesame has been indicated in the figure. From the presentwork, no transition was found that could be identified asdecaying from the said 5 − isomeric level to the groundstate of Pm which has been suggested to have a j π FIG. 9: The decay scheme obtained in the present work forthe newly identified 2.2(1) h isomeric state in
Pm. Theground state Q value is indicated. The spin parity of theisomer is suggested from shell model calculation (cf. Fig. 13). value of 2 − in the work of D. Bucurescu et al [22] and alsofrom the shell model calculation (cf. Section V). However,the present work could also not rule out the existence ofany such γ decay. It can be conjectured that the electro-magnetic decay from the proposed isomeric level mightbe highly hindered as it is possibly a low energy M3 orE4 γ transition. C. Measurement of γ intensities and calculation of logft values The intensity of β feedings from the proposed isomericstate has been obtained from the intensities of the in-volved γ transitions, measured in the present work. Forthis purpose, the detector efficiency was measured withthe standard Ba and
Eu sources, which has max-imum γ energy up to 1408 keV. Hence, for determiningthe efficiencies at higher energies upto 3038 keV, a lin-ear extrapolation of the efficiency curve was made. Ta-ble I shows the intensity values for all the transitions in Sm that are emitted following the decay of the pro-posed isomeric states in
Pm along with other relevantinformation. The intensities of the transitions have beenobtained from the singles data and by considering theintensity of the 334 keV (2 + → + ) transition as 100%.Considering the total observed β decay from this partic-ular isomer as 100%, the percentage of β -feeding to thecorresponding levels of Sm has been calculated fromthe intensity of the decaying γ transitions and are shownin Fig. 9. The logft values have been calculated for allthese β decay branches by considering the energy of theisomeric level in Pm at the following three differentvalues - 33.0 keV, as indicated by the shell model calcu-lation (cf. section V), 454(284) keV, as indicated from the β decay end point energy measurement(cf. section III D)and 150 keV which is close to the isomeric levels knownin Pm and
Pm nuclei. The calculation of logft val-ues have been performed by using the logft calculationprogram available in the NNDC database [30].The logft values obtained for the 2939.0, 2958.0 and3038.0 keV levels comes in the range of 5.4 to 6.5 forthree types of excitation energies of the excited states.This range of values of logft has been assigned mostlyfor allowed ∆J = 0,1 or first forbidden ∆J = 0,1 tran-sitions [31] and this leads to conjecture the J π values ofthese levels as (4 ± ,5 ± ,6 ± ). Hence, the assigned spin par-ity for the 3038 keV level, as obtained from the earlierbeta decay measurement [14], may be an artifact of con-sideration of the ground state beta decay of Pm to beresponsible for the population of this level.The logft value obtained for the 2507.5, 2551 and 2718keV levels comes about 6.1 to 6.8 as shown in table I.This value also corresponds to allowed and first forbiddenunique transitions [31]. Out of the said three levels, theJ π value for the 2507.5 keV level is known to be (3 + , 4 + )from the (n, γ ) work [14]. Consideration of the 3 + spinfor this level demands the beta decay feeding from theisomeric state to be of first forbidden unique type. In thepresent work, the spin parity of 4 + is proposed for thislevel based on the extracted beta decay logft value anda 5 − spin for the isomeric level. Also an assignment of3 − to the 2718 keV level (previously 2715 keV observedfrom (p, p (cid:48) ) reaction), that claims a second forbiddennon unique type beta decay, is not appropriate from theobserved logft value. Hence, either these two levels aredifferent and 2718 keV is a new level observed in thepresent work or the spin parity assignment to this levelhas to be different from 3 − . In the present work, thespin parity of (4 ± ,5 ± ,6 ± ) has, thus, been assigned to the2718 keV level. The spin parity of 2551 keV level is alsoproposed to be (4 ± ,5 ± ,6 ± ) as per the observed beta decay logft value.Hence, an accurate spin parity measurement is envis-aged for all these particular levels in Sm which wasnot possible in the present work.
D. Measurement of β decay End Point Energy The β decay end point energies have been measuredfor several decay branches of Pm to
Sm, followingthe techniques described in Ref. [24]. In order to gener-ate the γ − ( β + γ ) and γ − γ coincidence information,two RADWARE compatible matrices were made fromthe coincidence data obtained with two LEPS and four Clover HPGe detectors, in two different configurationsas described in section II. These LEPS events were com-pressed to 10, 20 and 40 keV/channel for the generationof β decay spectrum as and when required and with ap-propriate γ energy gates from the Clover events.The representative β -spectra obtained in the presentwork for the decay branches of Pm to
Sm havebeen shown in Fig. 10. The corresponding β -spectrahave also been obtained by using Monte Carlo simula-tion with the Geant3 simulation package [32] with onemillion events and the exact geometrical configuration.The results from the simulation has been normalized tomatch the experimental data points based on visual es-timation, with an emphasis in the energy range of 0.8E β to E β and is plotted with the corresponding experimen-tal results as shown in Fig. 10. The deviation of theexperimental results from the simulation at the low en-ergy side corroborates to the effects of background ap-pearing from the β -Compton and Compton-Compton co-incidences that could not be subtracted during genera-tion of β spectrum as has been described in Ref. [24].The Fermi-Kurie (FK) plots were generated from the ex-perimentally obtained β spectrum by using the built inroutine ‘FK-Energy’ included in the spectrometer codeLISE [33, 34]. The FK plots corresponding to the differ-ent β decay branches have been shown in Fig. 10 alongwith the β spectrum. The β end point energies havebeen obtained by fitting these plots and the results havebeen tabulated in Table II corresponding to different de-cay branches. The required corrections were made forthe attenuation in the Be window of the LEPS detectorsand both the corrected and uncorrected energies are men-tioned in Table II. The γ energy has also been indicatedin the table for each β branch which corresponds to thegating transition that was used for generating the β spec-trum. The endpoint energies have also been derived byperforming a chi-square analysis following the methodol-ogy of Ref. [24] and the representative chi-square plotshave been shown in Fig. 11. The χ values have been ob-tained by comparing the experimental data points withthe simulation at different end point energies. The ob-tained values have been fitted with a parabolic functionas shown in Fig. 11 and the minima of the obtained func-tion has been considered as the value of the end-pointenergy. The end-point energies, thus, obtained have alsobeen tabulated in table II. The error corresponds to theenergy difference required for the change in χ by 1.0.In the present work, the measurement of β decay end-point energies have been performed for the first time inthe decay of g Pm → Sm corresponding to severalexcited levels of the daughter. The β − γ coincidence anal-yses have also been performed for obtaining the possibleexcitation energy of the isomeric level in Pm by usinga higher binning of 80 keV/channel. The β spectrum cor-responding to the 1810 keV γ gate have been shown inFig. 12 which clearly shows that the obtained end pointenergy is higher than the value expected in case the tran-sition had originated from the decay of g Pm. The FK
TABLE I: Details of the excited levels and γ & β transitions relevant to the decay of isomeric level in Pm.The isomeric level in
Pm Levels in
Sm Decay E γ I γ I β a logft withdiff E x Ex. Energy(E x ) J π Lifetime Ex. Energy J π of m Pm(keV) (h) (keV) (ENSDF [14]) (Proposed) (keV) % of (%) 33 150 454334 keV keV keV keV(2 + → + )Expt: 3038.0 1,2 + (4 ± ,5 ± ,6 ± ) 3038.0 0.020(4) 7.7 5.5 5.8 6.5453(284) - 2.2(1) 2958.0 - (4 ± ,5 ± ,6 ± ) 2624.0 0.06(1) 15.4 5.4 5.7 6.3Shell Model: 2939.0 - (4 ± ,5 ± ,6 ± ) 1893.0 0.06(1) 15.4 5.5 5.8 6.433 5 − - 2718.0 3 − (4 ± ,5 ± ,6 ± ) 2384.0 0.05(1) 11.5 6.1 6.3 6.8Systematics: 2551.0 - (4 ± ,5 ± ,6 ± ) 1810.0 0.05(1) 23.1 6.1 6.3 6.7 ∼
150 - - 2507.5 3 + ,4 + (4 + ) 2174.0 0.05(1) 26.9 6.1 6.3 6.7 . a The intensities of β branching was calculated by considering thesum of all the observed decay of m Pm as 100%
FIG. 10: (Color Online) The representative β spectra ob-tained for some of the decay branches of g Pm → Sm.The experimental data points have been shown with blue cir-cles and the Red line shows the results obtained from Geant3simulation. The FK plots are shown with the obtained endpoint energies. analysis was performed and the β end point energy ob-tained has been shown in the Fig. 12 and in table II. Theexcitation energy of the proposed isomeric state in Pm FIG. 11: (Color Online) The representative χ plot for twoof the β decay branches of g Pm. The β decay end pointenergies obtained from χ and FK analyses are indicated. has been determined by comparing the β decay Q valuefor g Pm, the excitation energy of the levels in
Smand the obtained end point energy. The values come outto be 453(284) keV from the above analysis. The β spec-trum corresponding to the other transitions originatedfrom m Pm β decay could not be determined in the TABLE II: The β decay end point energies obtained in the present work with relevant details, as described in text.Decaying Final Level Branching Gating transition β EnergyNucleus Energy J π (Q β - E x ) Lit. F-K Anal. GEANT3(Q β ) (E x ) (uncorr) (corr) and χ Anal.(keV) (%) (keV) (keV) (keV) (keV) (keV) (keV) g Pm 334.0 2 + ≤
10 334 3120.0 - 2957 ±
73 3046 ±
73 3134 ± + ±
191 2733 ±
191 2673 ± + ±
219 2517 ±
219 2407 ± − ±
68 2266 ±
68 2330 ± ( − ) ±
153 1801 ±
153 1826 ± ±
105 1868 ±
105 1761 ± − ±
193 1615 ±
193 1462 ± ( − ) ±
180 1555 ±
180 1424 ± − ) 3.26 1214+1004+1066+1926+1519 1194.1 - 1509 ±
115 1594 ±
115 -2367.4 (3 + ) 1.04 2033 1086.6 - 1331 ±
221 1417 ±
221 1068 ± m Pm a ± ,5 ± ,6 ± ) 23.1 1810 903.4 - 1270 ±
284 1356 ±
284 -(3454 keV) a For the isomeric state, the branching has been considered fromFig. 9 of section III C. The Q value is mentioned for ground statedecay. present work, mainly due to low statistics.
IV. SYSTEMATICS OF LONG LIVEDISOMERIC STATES AROUND
PM AND THEPOSSIBLE STRUCTURE OF THE PROPOSEDISOMERS IN PM Most of the nuclei around
Pm show the presence ofone or more long lived isomeric state(s). The system-atics of these isomers around
Pm have been shownin table III and IV, where the isomeric levels having life-time ∼ µ s or more have been considered. The systematicsdepict that these isomers share some common features.Most of these isomers have half lives greater than or closeto that of the ground state and almost all of them exceptthree undergo β + , β − or EC decay. Also, in most of thecases, these isomers are negative parity levels and theirspins are higher at least by an unit of 3¯ h compared to the ground state spin. In table III and IV, the known con-figurations to the isomeric states in the odd-odd nucleiaround Pm are shown along with the available odd-proton and odd-neutron configurations taken from therespective odd-A neighbors.It is observed that the isomeric configurations in caseof the odd-odd Pm nuclei are mainly of two types. Forthe Pm nuclei with N ≤
83, single particle configurationslike πd ⊗ νh is proposed for the negative parity iso-mer in Pm and πh ⊗ νf configuration has beenconjectured for the positive parity isomer in Pm. Incase of more neutron rich Pm isotopes, these configu-rations are determined by the Nilsson configurations of π − [532] and ν − [521], that correspond to the deformed π h and ν f orbitals respectively, following the QuasiParticle Rotor Model (QPRM) calculations [44]. In thesystematics with N = 89, it is found that the configura-tions of these isomers in Z = 59 and Z = 63 are dominated0 TABLE III: Systematics of long lived isomers in odd-odd Pm nuclei neighboring to
PmIsomeric Level (odd-odd) proton ( π ) level odd-Z neutron ( ν ) level odd-NNucleus Ex. Energy J π τ & Nucleus Energy J π , τ Nucleus Energy J π , τ & Ref. (keV) Conf. Decay & Ref. (keV) Conf. & Ref. (keV) Conf. Pm 0.0 1 + Pm 0.0 (5/2 + ) Nd 0.0 3/2 + , 29.7m[36] - β + , (cid:15) [37] πd [37] -(425) 8 − − ), 180ms 231.7 11/2 − ,5.5h πd ⊗ νh β + , (cid:15) π − [541] νh Pm 0.0 1 + Pm 0.0 5/2 + 141
Nd 0.0 3/2 + , 2.49h[38] - β + , (cid:15) [39] πd [39] -883.17 (8 − ) 2.0ms 196.87 7/2 + , 0.23ns 193.68 1/2 + , 1.17ns- IT πg -628.62 11/2 − , 0.63 µ s 756.51 11/2 − , 62s πh νh Pm 0.0 5 − Pm 0.0 5/2 + , 265d Nd 0.0 7/2 − [40] - β + , (cid:15) πd νf + ) 0.78 µ s [41] 272.04 7/2 + , 1.06ns [41] 742.05 3/2 − , 2.8ps πh ⊗ νf IT πg − , 24ns πh Pm 0.0 1 − Pm 0.0 7/2 + 147
Nd 0.0 5/2 − [10] - β − [16] πg [16] -137.9 5 − , 6 − + , 2.5ns 49.92 7/2 − , 1.0ns- β − ,IT πg νh − , 27ns 190.29 (9/2 − ) πh νh Pm 0.0 1 − Pm 0.0 7/2 + 149
Nd 0.0 5/2 − [14] - β − π
72 + [404] ν − [523]& - 5 − + , 2.53ns [17] 493.3 11/2 − present - β − ,IT? π
52 + [402] ν − [505]work 240.21 11/2 − , 35 µ s πh Pm 0.0 1 + Pm 0.0 5/2 + , 28.4h Nd 0.0 3/2 + , 12.44m[11] π − [532] ⊗ ν − [532] β − [18] π
52 + [413] [18] π
32 + [651]+ π
32 + [402]150 4 − − , 89ps 57.67 (3/2) − π − [532] ⊗ ν − [532] β − π − [532] ν − [532]150+x 8 13.8m 255.6 3/2 + , 0.93ns 189.054 (3/2) − - β − ,IT π
32 + [411] ν − [521] Pm 0 (3, 4) 2.68m
Pm 0.0 5/2 − Nd 0.0 (3/2) − [12] π − [532] ⊗ ν − [521] β − π − [532] π − [521](210 ±
70) (0 − , 1 − ) 1.73m [19] 32.194 3/2 + , 1.2ns [19] 191.7 (5/2 − ) π − [532] ⊗ ν − [521] β − π
52 + [413] ν − [523]450.520 3/2 + π
32 + [411]
Pm 0.0 4( + ) 26.70s Pm 0.0 5/2 − Nd 0.0 (3/2 − )[13, 35] π − [532] + ν − [521] β − [43] 180.565 5/2 + [19]150.3 1 + < π
52 + [413] π − [532] − ν − [521] IT, α TABLE IV: Systematics of long lived isomers in N = 89 nuclei neighboring to
PmIsomeric Level (odd-odd) proton ( π ) level odd-Z neutron ( ν ) level odd-NNucleus Ex. Energy J π τ & Nucleus Energy J π , τ Nucleus Energy J π , τ & Ref. (keV) Conf. Decay & Ref. (keV) Conf. & Ref. (keV) Conf. La 0.0 (2 − ) 6.1s La 0.0 (5/2 + ) Ba[9] - β − , β − n [42] - [42](130) (6 − ) 9.8s 572.4 (11/2 − )- β − ,IT? - Pr 0.0 1 − Pr 0.0 (5/2 + ), 13.4m Nd 0.0 5/2 − [10] π
32 + [411] ⊗ ν − [523] β − [16] π
52 + [413] [16] -76.80 4 − − , 1.0ns π
52 + [413] ⊗ ν − [532] β − ,IT νf − ) νh Pm 0.0 1 − Pm 0.0 7/2 + 149
Nd 0.0 5/2 − [14] - β − [17] π
72 + [404] [17] ν − [523]& - 5 − + , 2.53ns 493.3 11/2 − present β − ,IT? π
52 + [402] ν − [505]work 240.21 11/2 − , 35 µ s πh Eu 0.0 3 − Eu 0.0 5/2 + 151
Sm 0.0 5/2 − [11] π
52 + [413] ⊗ ν − [505] (cid:15) , β + , β − [18] πd [18] ν − [523]45.59 0 − + + - (cid:15) , β + , β − πg νi − µ s 261.13 (11/2) − - ν − [505]65.29 1 − µ s- IT147.86 8 − π
52 + [413] ⊗ ν − [505] IT Tb 0.0 0( − , + ) 21.5h Tb 0.0 5/2 + 153
Gd 0.0 3/2 − [12] π
32 + [411] ⊗ ν − [521] (cid:15) , β + , β − [19] π
52 + [402] [19] ν − [521]or 80.72 7/2 + , 0.49ns 95.173 9/2 + , 3.5 µ s π
32 + [411] ⊗ ν
32 + [651] π
72 + [404] ν
12 + [660] ≤
25 3 − + ), 0.84ns 109.756 (5/2) − ,0.243ns π
32 + [411] ⊗ ν − [521] IT, (cid:15) , β + , β − π
32 + [411] ν − [523](200) 7 − − , 186 µ s 129.163 3/2 − , 2.52ns π
32 + [411] ⊗ ν − [505] IT, (cid:15) , β + πh ν − [532]171.188 (11/2 − ), 76 µ s ν − [505] Ho 0.0 4 − Ho 0.0 5/2 + 155
Dy 0.0 3/2 − [13] π
52 + [402] ⊗ ν − [521] (cid:15) , β + [43] π
52 + [402] [43] ν − [521]52.37 1 − + , < + , 51ns π
52 + [402] ⊗ ν − [521] IT π
72 + [404] ν
12 + [660](170) 9 + − , 0.88ms 136.319 5/2 − , < π − [523] ⊗ ν − [505] IT, (cid:15) , β + πh ν − [523]202.413 3/2 − , < ν − [532]234.33 11/2 − , 6 µ s ν − [505] FIG. 12: (Color Online) The β decay spectrum and corre-sponding FK analysis for the beta decay of m Pm, the 2.2 hisomeric state. by πg ⊗ νh configuration. In some of the cases with Z ≥
65, however, the configurations involving ν f or boththe ν h and π h are also seen to be existing.The above systematics clearly show that the isomericconfigurations in the odd-odd nuclei can be conjecturedby looking at the single particle configuration in theneighboring odd-Z and odd-N nuclei. Hence, the assign-ment of the configuration for the isomeric level in Pmcan be attempted by taking the above understanding intoconsideration. The single particle configuration which isfound to be active in the low lying states of odd-N nucleusneighboring to
Pm, viz.
Nd, is ν − [523], the Nils-son configuration corresponding to deformed ν f or-bital. In this nucleus, the state that corresponds to ν h is found at an excitation energy of 493 keV. In case ofthe odd-A Pm, viz., Pm and
Pm, the single particleconfigurations close to the ground state are the Nilssonconfigurations corresponding to π g , π d and π h .These are π
72 + [404] in case of
Pm ground state and π
52 + [402] in case of 114.3 keV state in
Pm. In
Pm,the major configurations are known to be π
52 + [413] forthe
52 + ground state, π − [532] for the − , 117 keV state, π
32 + [411] for the
32 + , 256 keV state and π
12 + [420] for the
12 + , 426 keV state. The first πh level in Pm lies at240 keV and is also an isomeric state. In case of
Pmthis proton configuration is observed at much lower exci-tation of 117 keV.Considering the available single particle orbitalsaround
Pm, it is understood that the involvement of πh particle or a νh hole in the configurations of the FIG. 13: The level energies for the excited levels of
Pmare compared with shell model calculation. The J π valuescorresponding to the each levels have been obtained from cal-culation. proposed isomeric state will make the excitation energyof the isomer very high. Hence, it may be conjecturedthat the low lying isomers with high spin may be one ofthe multiplets generated by involving the πg and the νf orbitals which give rise to the negative parity levels.There exist no theoretical model calculation to under-stand the excited energy levels of Pm. In the presentwork, a shell model calculation has been performed byusing OXBASH code [25] to examine the negative parityisomers in
Pm, as described in the following section V,with a restricted particle configuration in order to repro-duce the low lying negative parity levels in the nucleus.
V. SHELL MODEL CALCULATION
In order to find the structure of the low lying statesin
Pm, a Large Basis Shell Model (LBSM) calculationwas performed using the code OXBASH [25]. The calcu-lation considered
Sn as core and eleven protons weredistributed over the model space comprising of π (1 g ,2 d , 2 d , 3 s , 1h ) single particle orbitals along withseven neutrons over the ν (1 h , 2 f , 2 f , 3 p , 3 p , 1i )single particle orbitals. The calculations were carriedout using proton-neutron formalism in full valence spaceapplying particle restriction as shown in Table V. Thischoice was based on both the facts that increasing thenumber of combinations for the single particle orbitalswere not possible due to increasing dimension of the ma-trix and also the aim of the present work was to reproduce3the negative parity levels in comparison to the negativeparity ground state. The two-body matrix elements wereobtained from the well-known cwg interaction [45] sup-plied with the code OXBASH. The calculated excitationenergies of the negative parity states up to 300 keV exci-tation have been shown in Fig. 13, along with the exper-imental levels obtained via (p,n γ ) reaction in the work ofBucurescu et al [22]. A level by level comparison was notpossible as no experimental spin parity assignment forthese levels exists in literature. The comparison clearlyindicates that the ground state of Pm is likely to be2 − which has been reported as 1 − in ENSDF [14] andsuggested as 2 − in the work of D. Bucurescu et al [22].From the comparison, it is also observed that there isone 5 − state predicted at 33 keV excitation which liesbetween the 2 − ground state and the 3 − excited state.The major configurations of all the calculated levels werestudied and it is observed that although the proton con-figuration for both the ground state and the 5 − excitedstate is similar, the ground state wave function is dom-inated by the ν f configuration whereas contributionsfrom both the ν p and ν f orbitals are found to existas the major configurations of the 5 − state. However,the contribution of the configuration involving ν h inboth the ground state and the 5 − state is calculated tobe less than 1%.In the present work, the transition probability for theabove mentioned 5 − level to the 2 − ground state was cal-culated by considering the resultant 33 keV γ transitionas either of E4 or M3 in nature. The said transition prob-abilities come out to be 51.4 µ N f m for the M3 transitionand 8545 e f m for the E4 transition respectively. Thesevalues correspond to 1.3 × years (M3) and 2.5 × years (E4) of lifetimes respectively for γ decay from thepredicted 5 − level. These values corresponding to the150 keV energy for the isomer yield lifetime of 5.7 days(M3) and 31 days (E4) respecively. However, while con-sidering an energy value of 454 keV for the isomer theabove lifetimes go down to 3.5 m (M3) and 2.1 m (E4)respectively. The Weisskopf estimates for these respec-tive M3 and E4 transition rates were also calculated andcomes out about 1315 µ N f m (M3) and 39500 e f m (E4) respectively. These, in turn, corresponds to the γ decay half lives as 5.0 × years (M3) and 5.4 × years(E4) respectively. Hence, both from the half life valuesobtained from shell model as well as from single particleestimates, it can be concluded that the lowest 5 − levelin Pm will have almost no γ decay to the 2 − groundstate of Pm. Thus, the above calculations indicate thepresence of a 5 − , 33 keV isomer in Pm which under-goes β − decay to the excited states of Sm nucleus, asshown in Fig. 9.As pointed out in Section III C, the 5 − isomeric levelcould have various types of β decay modes, viz., the al-lowed Gammow-Teller (GT), first Forbidden (FF), FFunique and second forbidden transition . We attempted,using OXBASH, to calculate the logft values for the al-lowed GT transitions (characterised by ∆ l = 0, ∆ J = 0,1 (no 0 → π = 0) from the 2 − ground state and5 − isomeric state of Pm. For this calculation, first theenergy levels of
Sm have been calculated by using thesame formalism, core nucleus and the interaction matrixelements as used for
Pm, discussed above. The parti-cle restriction was required to truncate the model spaceso that the calculation could be performed with permit-ted dimension of the matrix. The available orbitals, theapplied particle restriction and the possible configura-tions for the positive and negative parity levels in
Smhave been given in table V. Although the said calculationcould reproduce some of the low lying positive parity lev-els, the excitation energies of the negative parity levelsin
Sm could not be reproduced well. This may bedue to the truncation of the model space which forcedin neglecting the configurations that associate more thanone particle in many of the orbitals, importantly in theunique parity π h and ν i orbitals, as understoodfrom the listed possible configurations in table V. Withthis limitation in the calculation, the configuration of the3 − , 4 − and 6 − levels in Sm were found to have beengenerated from one proton particle in π h . As per ourparticle restriction, this configuration is the first negativeparity configuration mentioned in table V. Now, any GT type β − decay from the ground state or the 5 − isomericstate in Pm to these negative parity levels in
Sm ispossible only by the conversion of one ν h neutron to a π h proton. For brevity, authors do not want to givedetails of these calculations, except to mention that theallowed GT decays from the 5 − isomeric state to the firstten 4 − ,5 − and 6 − states in Sm have logft values in therange of 7 - 11 and for the decay of the 2 − ground stateto the first and second 3 − state of Sm have logft values9.1 and 8.2 respectively. The measured logft (2 − g.s → − )is 9.65. Hence, this effort at least indicates the possibilityof the β − decay of the 5 − isomeric level and confirms itspresence in the level scheme of Pm.
VI. SUMMARY
The decay spectroscopy of
Pm has been performedby populating the nucleus with
Nd(p,n γ ) Pm reac-tion at E p = 8.0 MeV. The obseved γ rays were countedboth in singles and coincidence mode with the VENUSarray having six Compton suppressed Clover HPGe de-tectors. Following the decay curves of the observed tran-sitions and their γ − γ coincidence relationship could con-firm the presence of a long lived β -decaying isomer in Pm having half life 2.2(1) h. The logft analyses wereperformed using the intensities of different γ transitionswhich suggest modified J π assignment for the levels in Sm that are fed by the newly identified isomeric level.The β decay end point energies, corresponding to severaldecay branches of Pm ground state, have been mea-sured for the first time by using the β − γ coincidencetechnique with an array of two thin window LEPS andfour Clover HPGe detectors of the VENUS array. The4 TABLE V: The particle restrictions applied for the shell model calculation of
Sm levels. The possible configurations thosemay be responsible for the generation of +ve and -ve parity levels are indicated.Particle Restriction Possible configurationOrbitals Minimum Maximum Proton( π ) Neutron( ν )( g , d , d , s ) ( h ) ( f , h , f , p , p ) ( i )Nucleus: Pm-ve parity states :Proton ( π ) 2 d d s h h ν ) 2 f h f p p i Sm-ve parity states :Proton ( π ) 1 g d d s h ν ) 1 h f f p p i end point energy measurement for the isomeric β decayindicates the level energy of the isomer as 453(284) keV.The systematics of the configurations associated with thelong lived isomers, neighboring to Pm, have been stud-ied. Shell model calculation has been performed by usingOXBASH code that clearly indicates a 5 − isomeric levelat 33 keV excitation of Pm. The configuration of theisomer is suggested to be a mixture of π (1 g , d ) ⊗ ν p and π (1 g , d ) ⊗ ν f configurations. The transition probabilities calculated for this state to the 2 − groundstate, having a π (1 g , d ) ⊗ ν f configuration, suggestthat the electromagnetic decay half life of the isomer isgreater than 10 y and undergoes β decay. The contri-bution of the single particle configuration involving ν h orbital is conjectured to be present both in the groundstate and the 5 − isomeric state which makes the allowedGT type β decay possible from these two levels in Pm.The confirmation of the existence of 5 − isomeric level in5 Pm level scheme and the possibility of its β decaywere also obtained from the calculation of logft valuesusing OXBASH. The absence of experimental data forthe Pm nucleus warrants a further in-beam γ spectro-scopic measurement which has been planned as a futureexperimental outlook to this work. A detailed LBSMcalculation for this valence space is really challenging. VII. ACKNOWLEDGEMENT
The effort of the staffs and members of the K=130cyclotron operation group at VECC, Kolkata, is grate- fully acknowledged for providing high quality stable pro-ton beam. A. Saha is grateful for his UGC Fellowship(Ref. No:17-06/2012(i)EU-V) for carrying out his exper-iments at VECC, Kolkata. S. S. Alam would like to ac-knowledge the support from BRNS fellowship (SanctionNo. 2013/38/02-BRNS/1927 for PRF, BRNS, dated 16October 2013 ). The efforts of Mr. R. K. Chatterjee,RCD, VECC is acknowledged for target preparation. A.Chowdhury and Shaikh Imran of Physics lab, VECC areacknowledged for their effort to maintain the detectorsduring experiment. [1] F. Iachello, N. V. Zamfir, R. F. Casten, Phys. Rev. Lett. , 1191 (1980).[2] R. F. Casten et. al., Phys. Rev. C57 , R1553 (1998).[3] D. A. Meyer et al., Phys. Rev.
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