High-precision mass measurements for the isobaric multiplet mass equation at A = 52
D.A. Nesterenko, A. Kankainen, L. Canete, M. Block, D. Cox, T. Eronen, C. Fahlander, U. Forsberg, J. Gerl, P. Golubev, J. Hakala, A. Jokinen, V.S. Kolhinen, J. Koponen, N. Lalovi?, Ch. Lorenz, I.D. Moore, P. Papadakis, J. Reinikainen, S. Rinta-Antila, D. Rudolph, L.G. Sarmiento, A. Voss, J. ?ystö
aa r X i v : . [ nu c l - e x ] J a n High-precision mass measurements for the isobaric multiplet mass equation at A = 52 D.A. Nesterenko, ∗ A. Kankainen, L. Canete, M. Block,
2, 3, 4
D. Cox, T. Eronen, C. Fahlander, U. Forsberg, J. Gerl, P. Golubev, J. Hakala, A. Jokinen, V.S. Kolhinen, J. Koponen, N. Lalovi´c, Ch. Lorenz, I.D. Moore, P. Papadakis, J. Reinikainen, S. Rinta-Antila, D. Rudolph, L.G. Sarmiento, A. Voss, and J. ¨Ayst¨o
1, 6 University of Jyvaskyla, P.O. Box 35, FI-40014 University of Jyvaskyla, Finland GSI Helmholzzentrum f¨ur Schwerionenforschung GmbH, D-64291 Darmstadt, Germany Helmholtz Institute Mainz, D-55099 Mainz, Germany Johannes Gutenberg-Universit¨at Mainz, D-55099 Mainz, Germany Department of Physics, Lund University, S-22100 Lund, Sweden Helsinki Institute of Physics, P.O. Box 64, FI-00014 University of Helsinki, Finland (Dated: September 18, 2018)Masses of Co, Co m , Fe, Fe m , and Mn have been measured with the JYFLTRAP doublePenning trap mass spectrometer. Of these, Co and Co m have been experimentally determinedfor the first time and found to be more bound than predicted by extrapolations. The isobaricmultiplet mass equation for the T = 2 quintet at A = 52 has been studied employing the new massvalues. No significant breakdown (beyond the 3 σ level) of the quadratic form of the IMME wasobserved ( χ /n = 2 . χ /n = 1 . T = 2 isobaric analogue state in Co have been determined to be 374(13) keVand 2922(13) keV, respectively. The Q value for the proton decay from the 19 / − isomer in Cohas been determined with an unprecedented precision, Q p = 1558 . Co and Ni relevant for the astrophysical rapid proton capture process have beenexperimentally determined for the first time.
PACS numbers: 21.10.Dr, 21.10.Sf, 27.40.+z
I. INTRODUCTION
Assuming a charge-independent nuclear force, the iso-baric analogue states (IAS) in an isobaric multipletare degenerate. Their mass differences are due toCoulomb interaction and the neutron-proton mass differ-ence. According to the Isobaric Multiplet Mass Equation(IMME) [1], the masses of IASs in a mass multiplet withan atomic mass number A and isospin T should lie on aparabola: M ( A, T, T Z ) = a ( A, T ) + b ( A, T ) T Z + c ( A, T ) T Z , (1)where the coefficients a , b and c are interpreted as beingthe scalar, vector and tensor Coulomb energies. High-precision Penning-trap mass measurements have offerednew possibilities to investigate the validity of the IMME,and have revealed a breakdown in the quadratic form ofthe IMME in a few cases, such as for A = 8 [2], A = 9[3], A = 21 [4], A = 31 [5], A = 32 [6, 7], and A = 35[8]. In general, however, the IMME seems to describewell the masses of isospin multiplets, and it has thereforebeen widely used to predict the masses of the most exoticmembers of the multiplets.Sometimes the quadratic form of the IMME (Eq. 1) isnot sufficient to describe the masses in an isobaric multi-plet but a cubic ( dT Z ) or even a quartic coefficient ( eT Z )is required. The T = 3 / ∗ dmitrii.nesterenko@jyu.fi when entering into the f / shell [9, 10]. On the otherhand, the quadratic IMME at A = 53 has been recentlyrevalidated with a reduced χ of 1.34, and the cubic co-efficient has been found to be rather small, d = 5 . d = 39(11) keV obtained in Ref.[12].The T = 2 quintets have not been experimentally ex-plored in the heavier mass region but could provide fur-ther insight into the possible trend in the cubic coeffi-cients. In this paper, we have experimentally determinedthe masses for Co, Fe, and Mn, which are mem-bers of the T = 2 isobaric quintet at A = 52 togetherwith Cr and Ni. Previous IMME evaluations for thequintet have suggested that a large non-zero cubic coeffi-cient, d = 28 . Co and Ni.Thus, the mass of Co, determined here experimentallyfor the first time, is pivotal for testing the IMME andinvestigating whether there is a trend towards larger cu-bic coefficients for nuclei in the f / shell forming T = 2quintets.In addition to the ground states of Co, Fe, Mn,we have studied isomeric states in Co and Fe as sum-marized in Table I. The isomeric state of Co is of spe-cial interest because it can be used to determine themass of the T = 2 IAS in Co. The current knowl-edge of the T = 2 IAS in Co is based on β -decay stud-ies of Ni [13, 14]. Two prominent β -delayed protongroups with center-of-mass energies of 1057(11) keV and1349(10) keV [13] have been observed from the IAS. Sim-ilar proton energies at 1048(10) keV and 1352(10) keV TABLE I. Properties of the nuclides studied in this work. T / is the half-life, I π the spin-parity and E x the excita-tion energy of the isomeric state. The values estimated fromisospin symmetry or from systematic trends from neighboringnuclides with the same Z and N parities are marked by T / I π E x (keV) Co 104(7) ms 6 + Co m a + Fe 8.275(8) h 0 +52 Fe m + Mn 5.591(3) d 6 +a Authors in Ref. [19] do not have specific evidence for Co m . have been determined in a more recent work [14]. Theproton peaks have been attributed to the decay of theIAS to the ground state and first excited states in Feknown from in-beam γ -ray spectroscopy [15, 16]. Theexcitation energy of the IAS can thus be determined asa sum of the observed proton energy and the proton sep-aration energy of Co. On the other hand, the excita-tion energy of the IAS can be derived from the observed γ - γ cascade ( E γ = 2418 . E γ = 142 . β -decaying 2 + iso-mer in Co. However, a discrepancy was found betweenthe IAS energies of Co derived from the proton and γ -decay data when tabulated mass values were appliedfor Co and Co m in Ref. [13]. The γ - γ -cascade tothe isomeric state in Co resulted in an IAS about 600keV higher than the proton data leading to the groundstate of Fe. Therefore, it was proposed [13] that theground state mass excess of Co might be too high inthe Atomic Mass Evaluation [17]. With our direct massmeasurements of Co and Co m , we can now determinethe excitation energy of the isomeric state, and thereforeinfer the excitation energy of the T = 2 IAS.The masses of Co and Fe discussed in this pa-per were measured in conjunction with a post-trap spec-troscopy experiment dedicated to the study of protonradioactivity from the 19 / − isomer in Co. It is theisomer from which the first observations of proton ra-dioactivity were made about 45 years ago [21–23]. In thisrespect, the mass of Fe is important as when combinedwith the former, precise mass measurements of Co and Co m [24], as it provides a precise, external calibrationpoint for proton-decay spectroscopy.The nuclei studied in this work are also relevant forstudies of the astrophysical rapid proton capture ( rp )process occurring, for example, in type I X -ray bursts[25, 26]. The proton capture rates as well as theirinverse photodisintegration reactions depend sensitivelyon the reaction Q values [27]. In particular, the ra-tios of Fe( p, γ ) Co- Co( γ, p ) Fe and Co( p, γ ) Ni- Ni( γ, p ) Co reactions affecting the route towards heav-ier elements have been studied with experimental Q val-ues for the first time. II. EXPERIMENTAL METHOD
The isotopes of interest were studied in two separateexperiments at the Ion-Guide Isotope Separator On-Line(IGISOL) facility [28]: Co and Fe in April and Mnin August 2015. A 50-MeV proton beam from the K-130 cyclotron impinging into an enriched 1.8-mg/cm -thick Fe target was used to produce Co and Fevia fusion-evaporation reactions, whereas for Mn a 40-MeV proton beam was applied. The reaction productswere stopped in helium gas, extracted and guided to-wards the mass separator using a sextupole ion guide(SPIG) [29] before acceleration to 30 kV. A good frac-tion of the ions are singly-charged, and the mass num-ber A = 52 could be selected using a 55 ◦ dipole mag-net. A gas-filled radio-frequency quadrupole cooler andbuncher [30] cooled the ions and converted the continuousbeam into narrow ion bunches which were injected intothe JYFLTRAP double-Penning-trap mass spectrometer[31]. In the first trap, ions were cooled, centered andpurified via a mass-selective buffer gas cooling technique[32]. The masses of ions with charge-to-mass ratio q/m were measured in the second measurement trap by de-termining their cyclotron frequency ν c = qB/ (2 πm ) ina magnetic field strength B via a time-of-flight ion cy-clotron resonance (TOF-ICR) technique [33, 34].The measurements of the ions of interest were sand-wiched by similar measurements of the reference ion Cr + , which were linearly interpolated to the time of theactual measurement of the ions of interest to determinethe magnetic field strength. The atomic masses were de-rived from the cyclotron frequency ratio r = ν c,ref /ν c between the reference ion Cr + and the ion of interestvia m = r · ( m ( Cr) − m e ) + m e .Ion-ion interactions were studied by performing count-rate class analysis [35] for the determined frequencies,except for Co and Co m , for which it was not necessarysince most of the bunches contained only one ion. Nosignificant differences were observed when the count-rateclass analysed frequency ratios were compared with theresults obtained by restricting the number of ions to oneto five ions/bunch. Thus, limiting the number of ionsto one to five ions/bunch is sufficient to avoid possiblefrequency-ratio shifts due to ion-ion interactions for thepresent uncertainty level.The uncertainties due to temporal fluctuations in themagnetic field, δB/B = 8 . × − /min × ∆ t [min][36] were negligible compared with the statistical uncer-tainties of the measured frequency ratios. For mass dou-blets with the same A/q , the mass-dependent and sys-tematic uncertainties resulting from field imperfectionscancel in the frequency ratio [37]. The internal and ex-ternal uncertainties of the measured frequency ratios [38]were compared and the ratio was found to be close tounity. The larger of the two values was used for theweighted mean of the frequency ratios.For Co, the trap cycle was kept as short as possibledue to the short half-lives of Co + and Co m + (see Ta- FIG. 1. (Color online) Time-of-flight ion cyclotron resonancespectrum for Co + and Co m + with a 100 ms RF excitationtime. The solid red line is a fit of the theoretical curve to thedata points. ble I). A single, 100-ms-long quadrupolar radiofrequency(RF) excitation applied in the second trap was suffi-cient to resolve the ground-state Co + and isomeric-state Co m + ions as shown in Fig. 1. Although each Co measurement took around three hours, the uncer-tainty due to temporal fluctuations in the magnetic fieldwas still much less than the statistical uncertainty of thefrequency ratio ( ≈ × − ).For Fe + , Fe m + , and Mn + , the following Ramseyexcitation patterns [39, 40] were applied: 25 ms (On) -350 ms (Off) - 25 ms (On) for Fe + and Fe m + , and25 ms (On) - 750 ms (Off) - 25 ms (On) for Mn + . Thedata for these nuclides were collected interleavedly [41]:after one frequency scan for the reference ion, a few fre-quency scans were collected for the ions of interest. Thispattern was repeated as long as required for sufficientstatistics (typically for a few hours). Such interleavedscanning reduces the uncertainties due to time-dependentfluctuations in the magnetic field considerably. Becauseof the high excitation energy of the isomeric state Fe m ( E x = 6958 . Fe + and Fe m + are givenin Fig. 2.For the cyclotron frequency measurements of Mn,a Ramsey cleaning technique [42] was additionally ap-plied to resolve the 6 + ground state and the 2 + isomericstate with excitation energy 377.749(5) keV [18]. A dipo-lar excitation pulse with a Ramsey pattern 5 ms (On) -25 ms (Off) - 5 ms (On) in the second trap excited themotion at the modified cyclotron frequency of unwanted,isomeric-state ions, but the ions of the Mn ground statewere unaffected. Following this excitation step, only theground-state Mn + ions could pass through the 1.5-mmdiaphragm back to the first trap for recooling and recen- tering before the actual mass measurement in the secondtrap. III. RESULTS AND DISCUSSION
The results of the mass measurements are summarizedin Table II. Detailed discussion related to the masses of Co, Fe and Mn can be found from sections III A,III C, and III E, respectively. In addition, the results forthe excitation energies of the isomer Co m and the T = 2IAS in Co are discussed in section III B. The impacton the proton separation energy of Co is explored insection III D. In section III F, the IMME for the T = 2quintet at A = 52 is studied in detail. Implications forthe rapid proton capture process are briefly discussed insection III G. A. The masses of Co and Co m The mass of Co has never been measured before:only an extrapolated value was given for it in the AtomicMass Evaluation 2012 (AME12) [43]. In this work,five cyclotron frequency ratios for the ground state andfour ratios for the isomeric state were determined (seeFig. 3). The weighted means of the frequency ra-tios are 1 . . Co + and Co m + , respectively. The first experimental mass-excess values for Co and Co m , − . − Co is more bound than predicted by theatomic mass evaluation. On the other hand, our exper-imental value for the Co ground state is significantlyhigher than the estimation based on mirror symmetryand known β -delayed proton data, − B. Excitation energies for the isomer Co m andthe T = 2 IAS in Co Based on the ground and isomeric state masses mea-sured in the experiment, an excitation energy of E x =374(13) keV was determined for the isomer Co m . Thisagrees well with the extrapolated value in the NUBASE2012 evaluation, E x = 380(100) E x = 377 . Mn.The spins and parities for the lowest states in Cohave not been experimentally verified. Thus, we per-formed large-scale shell-model calculations with the full f p shell ( t = 7) to study the lowest levels in Co. Thecalculations were performed without isospin-symmetrybreaking terms (ISB) for FPD6, GXPF1A and KB3G, aswell as with ISB for KB3G (for details, see e.g. Ref. [45]).All calculations are in line with a 6 + ground state anda 2 + first excited (isomeric) state (see Fig. 4). However, FIG. 2. (Color online) Time-of-flight ion cyclotron resonances of Fe + (left) and Fe m + (right) with 25 ms (On) - 350 ms(Off) - 25 ms (On) Ramsey excitation pattern. The solid red line is a fit of the theoretical curve to the data points.TABLE II. The weighted average cyclotron frequency ratios, r , and mass-excess values, ME JY F L , determined in this work incomparison with the mass-excess values from AME12 [43]. The atomic mass excess value -55416.1(6) keV for Cr [43] wastaken to calculate the mass excesses of the studied nuclides from the frequency ratios. The mass-excess values from AME12[43] are given in the fourth column. The differences between the JYFLTRAP and the AME12 mass values are given in the fifthcolumn.Nuclide r ME
JY F L (keV) ME AME (keV) JYFL-AME12 (keV) Co 1.00043584(14) -34331.6(66) -33990(200) Co m Fe 1.0001464894(28) -48330.67(60) -48332(7) 1(7) Fe m Mn 1.0000973119(13) -50709.97(59) -50706.9(19) -3(2) all models have problems with producing the observedenergy split between the 6 + and 2 + states. On the otherhand, the experimental mirror energy differences betweenthe 2 + and 1 + states in Co and Mn determined in thiswork, − − − Co m has important con-sequences for studying the T = 2 isobaric multipletat A = 52. Namely, the excitation energy of the T = 2 IAS in Co can be determined based onthe γ - γ cascade from the T = 2 IAS to the isomer[13]: E IAS ( Co) = E γ (2418.3(3) keV)+ E γ (142.3(1)keV)+ E ( Co m ) = 2934(13) keV. However, a recent ex-periment performed at GANIL [14] obtained a signifi-cantly different energy for the most intense gamma tran-sition, E γ = 2407(1) keV, and a slightly smaller en-ergy for the second transition, E γ = 141(1) keV. Withthese values, E IAS ( Co) = 2922(13) keV is obtained(see Fig. 5). For both cases, the γ - γ cascade is taken tofeed the (2 + ) isomer, i.e. Co m .On the other hand, the energy for the T = 2 IAS in Co can be determined based on the proton separationenergy of Co and β -delayed protons observed from theIAS with center-of-mass energies of E p,CM = 1349(10)keV [13] and E p,CM = 1352(10) keV [14]. Our newground-state mass for Co results in a proton separa-tion energy S p ( Co) = 1418(11) keV, when the massvalues for Fe and H are taken from Ref. [43]. Assumingthe observed protons come from the IAS, the excitationenergy should be E IAS ( Co) = E p,CM + S p ( Co) =2767(15) keV [13] or 2770(15) keV [14]. Thus, the ob-tained excitation energy is 167(20) keV [13] or 152(20)keV [14] lower than that obtained via the γ - γ cascade.The difference of around 150 keV between the exci-tation energies of the IAS is much smaller than the ex-citation energy of the first excited state in Fe, E x =253 . γ -transition of around 150keV in Fe is also unlikely as it should have been ob-served in coincidence with the intense proton peaks. Thediscrepancy could be explained if the mass of Fe wasaround 150 keV off in AME12 [43]. However, it is knownwith a precision of 9 keV and is based on two indepen-dent measurements [47, 48]. Hence, the observed pro-tons are most likely emitted from a state below the IAS
FIG. 3. Cyclotron-frequency ratios measured for Co (left) and Co m (right) in this work. The gray-shaded bands representthe total uncertainty of the averaged frequency ratio.FIG. 4. Lowest levels observed in Mn and Co in comparison with large-scale shell-model calculations using the full fp shell, t = 7. Shown are the results obtained with FPD6, GXPF1A and KB3G without isospin-symmetry breaking terms (ISB), andwith ISB for KB3G. (see Fig. 5).Thus, we obtain E IAS ( Co)=2934(13) keV [13]for the excitation energy of the IAS in Co, or E IAS ( Co)=2922(13) keV, if more recent values fromOrrigo et al. [14] are used. Both values are much closerto the excitation energy of the T = 2, 0 + mirror state in Mn, E x = 2926 . γ -transition energies, 2418.3(3) keV[13] and 2407(1) keV [14]. There is no clear explana-tion for the difference and a new measurement of the γ - γ cascade would be required to obtain a more accurateexcitation energy for the IAS. C. The masses of Fe and Fe m Altogether 36 cyclotron frequency ratios for the groundstate Fe and seven ratios for the 12 + isomeric state Fe m were determined (see Fig. 6). The weightedmeans of the frequency ratios, 1 . . − . − . Fe has been mainly based onthe β + decay of Fe and the Fe( p, t ) Fe reaction Q value (see Fig. 7). The excitation energy for the isomer, E x = 6960 . E x = 6958 . E γ transitions fromthis 12 + yrast trap in Fe [49]. It should be noted thatthe relative uncertainties of the measured frequency ra-tios, 2 . × − and 5 . × − for Fe + and Fe m + ,respectively, are much smaller than the relative uncer-tainty in the reference mass δm/m ( Cr) = 1 . × − .Therefore, the precision in the determined mass-excessvalues could be further improved via a more precise mea-surement of the reference Cr.
FIG. 5. (Color online) Partial decay scheme for the β + decay of Ni with the proton separation energy S p ( Co) and theexcitation energy for the isomeric state 2 + from this work. All energies are in keV. The energies for the γ transitions (shownin blue) and the proton energy E p are taken from Ref. [13] and [14] (in curly brackets). The energies for the 1 + state and theIAS are based on our value of E x ( Co m ) and the γ -transitions from Refs. [13] and [14] (in curly brackets). The parametersof levels in Fe are taken from Ref. [46]. The proton line highlighted in red was previously thought to originate from the IASbut this work has shown it comes from a state lower than the IAS.FIG. 6. Cyclotron-frequency ratios measured in this work for Fe + (left) and Fe m + (right). The gray-shaded bands representthe total uncertainty of the averaged frequency ratios. D. Proton separation energy of Co and theenergy of the protons emitted from Co m The mass of Fe is relevant for determining the pro-ton separation energy of Co and, in particular, for the energy of the protons emitted from the 19 / − high-spinisomer Co m [21–23]. By combining the newly mea-sured Fe mass-excess value with the earlier JYFLTRAPmass measurements of Co ( − . Co m ( − . F e ( + ) ( ) F e ( + ) ( ) * F e ( p ,t ) ( ) A M E J Y F L T R AP -10-5051015 M E J Y F L - M E L I T ( k e V ) FIG. 7. Comparison of previous mass-excess values of Fe tothe JYFLTRAP value determined in this work. The AME12evaluation [50] is mainly based on the β + decay of Fe [51]and the Fe( p, t ) Fe reaction Q value [52]. For the β -decayvalue denoted by an asterisk, the JYFLTRAP value of Mnhas been used. energy S p ( Co)=1615.6(16) keV and a center-of-massenergy E p,CM ( Co m )=1558.8(17) keV for the protonsfrom the high-spin isomer to the ground state of Feis obtained. The proton separation energy is in a per-fect agreement with the AME12 value S p ( Co)=1615(7)keV [43] but about four times more precise. Our value forthe energy of the protons emitted from Co m is around20 times more precise than obtained via proton-decayexperiments E p,LAB = 1530(40) keV [21], E p,LAB =1570(30) keV [22], and E p,CM = 1590(30) keV [23]).Thus, we have demonstrated that Penning-trap measure-ments can provide precise calibration values for charged-particle spectroscopy. E. The mass of Mn A frequency ratio r = 1 . Mn + (see Fig. 8). This yields an atomicmass-excess value of − . Mn. TheJYFLTRAP value is 3(2) keV higher than the AME12value ( − . Q -valuemeasurement of Fe( d, α ) Mn [53] which gives a mass-excess value of − . Mn is anexample of a nuclide close to stability whose mass hasnot been determined with modern techniques. The ob-served difference to the AME12 value shows that it isworthwhile to check such mass values which are based onmeasurements performed decades ago. Although our newvalue disagrees with Ref. [53], it is in a rather good agree- ment with other, less precise experiments done on Mn(see Fig. 9). Of these, the β + decay of Mn [54] andthe value based on the Cr( He , t ) reaction [55] agreevery well with the present value. A more precise massvalue for the reference Cr would be beneficial for Mnas well since the relative uncertainty of the frequency ra-tio, 1 . × − , is nine times smaller than the relativeuncertainty of the reference mass. FIG. 8. Cyclotron-frequency ratios measured in this work for Mn + . The gray-shaded band represents the total uncer-tainty of the averaged frequency ratio.FIG. 9. Comparison of Mn mass-excess values from pre-vious works and the AME12 [43] to the JYFLTRAP valuedetermined in this work. Previously, the mass of Mn hasbeen studied via β + decays of Fe [51] and Mn β + de-cay [54, 56], Cr( p, n ) [57], Cr( He , t ) [55], as well as via Fe( d, α ) reactions (see Refs. [58] (1967a), [59] (1967b), and[53].)
TABLE III. Excitation energies, E x,IAS , and mass-excess val-ues, ME IAS , for the J π = 0 + , T = 2 isobaric analog states at A = 52. For Fe and Mn, the mass-excess values for theIAS are based on the mass-excess values from this work andexcitation energies from Ref. [18]. For Co, the mass excessfor the IAS is based on the mass of Co m measured in thiswork and the γ -ray energies from Ref. [14].Nuclide T Z E x,IAS (keV) ME IAS (keV) Ni -2 0 -23474(700) Co -1 2922(13) -31410(11) Fe 0 8561(5) [18] -39769.7(50) Mn 1 2926.0(5) [18] -47783.97(77) Cr 2 0 -55418.1(6) [43]
F. The IMME for the T = 2 quintet at A = 52 The IMME was studied for the T = 2 quintet at A = 52using the mass values for Co m , Fe, and Mn deter-mined in this work together with the mass values of Crand Ni adopted from AME12 [43] as summarized in Ta-ble III. Our mass-excess value for the isomer Co m andthe energies of the γ - γ cascade observed from the IAS inRef. [14] (see Sect. III B) were used for the mass excess ofthe IAS in Co. The excitation energy of the T = 2 IASin Fe, 8561(5) keV [18], is based on a study employingthe Fe( p, t ) reaction [60], where a doublet of two 0 + lev-els separated by around 4 keV were observed. For Mn,the IAS at 2926.0(5) keV [18] has been identified in manyexperiments with the main contribution coming from a Cr( p, nγ ) study [61] where 2379.5(5) keV γ -rays fromthe IAS to the 1 + state at 546.438(6) keV were observed.The results for the error-weighted quadratic and cubicfits for the IMME are given in Table IV. The reduced χ of 2.4 for the quadratic fit is well above one. However, thecubic coefficient d = 6 . ± σ limitfrom zero and, thus, compatible with zero. We checkedthe quadratic fit also without Ni, which is based onlyon the extrapolation of the mass surface [43]. A slightlyhigher reduced χ value, χ /n = 3 .
3, and a cubic coeffi-cient of d = 5 . eT Z is assumed instead of a cubic term,a coefficient e = 2 . d = 28 . c from quadratic to cubicfits were observed [9]. We can now confirm that thesehave been due to erroneous data used in the fits. Priorto this experiment, it was assumed that protons with E p,CM = 1352(10) keV [14] originate from the T = 2IAS in Co. Using the mass-excess values of Fe and H from AME12 [43] together with the proton energy, amass-excess value of − Cois obtained. This differs by 152(17) keV from the valuedetermined in this work. For comparison, we performedsimilar IMME fits using the AME12 data for the ground-state masses and − Co.
TABLE IV. Coefficients and the reduced χ values for thequadratic and cubic IMME fits (in keV) for the T = 2 quintetat A = 52. Quadratic Cubica -39777.1(30) -39769.4(50)b -8192.9(46) -8192.8(46)c 186.2(16) 172.2(75)d 6.0(32) χ /n The reduced χ for the quadratic fit was 18 . d = 29 . Nimight be higher, meaning it could be less bound thanpredicted in the AME12.The cubic coefficients for the T = 3 / T = 2 quintets have been plotted in Fig. 11. Earlier, atrend of increasing cubic coefficients after entering the f / shell has been observed. However, a recent observa-tion of γ -rays from the IAS in Co following the β decayof Ni showed that the IAS is lower than anticipated by β -delayed proton data from Ref. [13]. With the new ex-citation energy, the cubic coefficient for the A = 53 quar-tet is d = 5 . T = 2 quintet at A = 52, d = 6 . Ni[13, 14] does not originate from the IAS in Co but froma state below it. This is also understandable since thebeta-delayed protons from the T = 2 isobaric analoguestate decaying to the ground state of Fe ( T = 1 / T = 1 and T = 2 states in Co or T = 1 / T = 3 / Fe, respectively.In conclusion, there is no evident change in the cubiccoefficients after entering the f / shell. Although thecoefficients are on the order of some keV, they are stillcompatible with zero within the ± σ limit. The massdetermination of the most exotic member of the T = 2multiplet at A = 52, Ni, would be crucial to providea more stringent test of the IMME at the heavier massregion.
G. Implications for the rapid proton captureprocess
The rp process proceeds along nuclei close to the N = Z line mainly via proton captures and β + decays, FIG. 10. (Color online) Differences of the mass-excess valuesof the T = 2 quintet at A = 52 to the quadratic and cubicfits from this work (see Table IV) or from AME12, using themasses of Fe and H together with the E p,CM = 1349(10)keV from [13] for the IAS in Co.
10 20 30 40 50-1001020304050
T=3/2 T=2 A=53 (Su et al.) A=52 (this work) d ( k e V ) Mass number A
FIG. 11. (Color online) Cubic coefficients d for the T = 3 / T = 2 quintets from Ref. [9], with A = 21 and A = 31 updated from recent publications [4] and [5]. Thecubic coefficient observed in this work for the A = 52 quintet, d = 6 . A = 53 quartet, d = 5 . et al. [11], andconsistent with zero. These new values are highlighted in red. resulting in a thermonuclear runaway and a sudden re-lease in energy observed, for example, in type I X-raybursts [25, 26]. Proton-capture Q values are essentialfor modeling the rp process as they determine the path:the ratio of inverse photodisintegration reactions to thetotal proton-capture rate ( λ γ,p /N A h σv i ) depends expo-nentially on the proton-capture Q values. Those can havea significant effect as demonstrated in Ref. [27].With the new mass-excess value determined inthis work for Co, proton-capture Q values for Fe( p, γ ) Co and Co( p, γ ) Ni can be experi- mentally determined for the first time. Thenew values, Q ( Fe( p, γ ) Co)=1418(11) keV and Q ( Co( p, γ ) Ni)=2588(26) keV, differ significantlyfrom the extrapolated values of 1077(196) Cois around 340 keV more proton bound and Ni less pro-ton bound than expected from the extrapolations of themass surface in AME12.In Fig. 12 we show the effect of the new Q values onthe photodisintegration versus proton capture rate ratio.With the new Q values, the route via Co is more likelythan before as Co is more proton-bound. For example,when the experimental Q value is used instead of theextrapolated AME12 value, photodisintegration rates on Co are suppressed by a factor of around 50-3000 com-pared to the proton-capture rates on Fe at tempera-tures below 1 GK. Although more detailed rp -processcalculations would be needed to find out the effect on thewhole rp process, the big change in the Co mass valuesignificantly changes the calculations related to the pro-ton captures and photodisintegration reactions involving Co.
IV. CONCLUSIONS AND OUTLOOK
In this work, we have performed direct mass mea-surements of Co, Co m , Fe, Fe m , and Mn withthe JYFLTRAP double Penning-trap mass spectrometer.The masses of Co and its isomer Co m have been ex-perimentally determined for the first time. The new massvalue for Co is significantly lower than that obtainedvia extrapolations in the AME12 showing that it is morebound than expected. The obtained excitation energy ofthe isomer, E x = 374(13) keV, is in good agreement withits analog state in Mn with E x = 377 . I π = 2 + for the isomeric state.An important consequence of the mass measurementsof the Co ground and isomeric states is that the massfor the T = 2 IAS can be determined using data from β decay of Ni [13, 14]. We have found that the protonsassumed to originate from the IAS in Ref. [13] must comefrom a state at around 2770(15) keV in Co, which issignificantly lower than the excitation energy determinedfor the IAS in this work, E x = 2922(13) keV, based onthe observed γ - γ cascade [13, 14] from the IAS to the (2 + )isomeric state in Co. The new excitation energy for theIAS agrees well with the analogue state in the mirror nu-cleus Mn, 2926.0(5) keV. It is interesting that the IASseems to decay only via γ transitions since the protondecays are isospin-forbidden, whereas the state below ithas a substantial proton branch but no observed γ tran-sitions. In the future, further experiments to confirmthe state from which the observed protons come fromare needed. In addition, the discrepancy between themeasured γ -transition energies of 2418.3(3) keV [13] and2407(1) keV [14] should be studied to improve the accu-0 FIG. 12. (Color online) Ratio of the photodisintegration ( γ, p )to the proton-capture rate N A h σv i for (a) Fe( p, γ ) Co- Co( γ, p ) Fe and (b) Co( p, γ ) Ni- Ni( γ, p ) Co reac-tions. The gray-shaded regions show the uncertainty bandrelated to the AME12 Q value. The Q -value related uncer-tainties for the JYFLTRAP results are invisible on this scale. racy of the T = 2 IAS in Co.The masses of Fe, Fe m , and Mn have been de-termined with a much higher accuracy than in AME12.The precision in the Fe mass value has been im-proved by a factor of around twelve, which allows aprecise determination of the proton separation energyof Co, S p ( Co)=1615.6(16) keV. In addition, the en-ergy of the protons emitted from the high-spin isomer in Co m to the ground state of Fe has been determinedwith unprecedented precision, E p,CM = 1558 . Fe, Co, and Co m at JYFLTRAP have therefore delivered an external calibra-tion value for proton-decay experiments.Whereas the masses of Fe and Fe m agree well withAME12, Mn shows a deviation of − Cr would improve the precision of the massvalues for Fe, Fe m , and Mn determined in thiswork. Presently, the mass of Cr is linked to Mn via Cr( n, γ ) Cr( n, γ ) Cr( p, γ ) Mn [50], where Mn hasbeen measured with respect to Rb at ISOLTRAP [62].The first mass measurement of Co provides alsofirst experimental proton separation energies for Coand Ni, 1418(11) keV and 2588(26) keV, respectively.These are also the proton-capture Q values for the protoncaptures Fe( p, γ ) Co and Co( p, γ ) Ni, which affect rp -process calculations. Since Co has been found to bemore bound than predicted in AME12, photodisintegra-tion reactions on Co are not so dominant as previouslypredicted, thus making it more likely that the rp processproceeds via Fe( p, γ ) Co.Finally, we have thoroughly studied the IMME for the T = 2 quintet at A = 52 using the new mass valuesdetermined in this work. The quadratic fit results in χ /n = 2 .
4, which corresponds to around 10 % proba-bility that the quintet can be described with a parabola.However, the cubic coefficient, d = 6 . d = 28 . T = 3 / A = 53[11]. The new value does not suggest a trend of increas-ing cubic coefficients when entering the f / shell. Inthe future, a mass measurement of Ni would providea possibility for a more stringent test of the IMME at A = 52. ACKNOWLEDGMENTS
This work has been supported by the Academy of Fin-land under the Finnish Centre of Excellence Programme20122017 (Nuclear and Accelerator Based Physics Re-search at JYFL) and the Swedish Research Council (VR2013-4271). A.K., D.N., and L.C. acknowledge supportfrom the Academy of Finland under grant No. 275389. [1] S. B. Weinberg, S. and Treiman,Phys. Rev. , 465 (1959).[2] R. J. Charity, J. M. Elson, J. Manfredi, R. Shane, L. G.Sobotka, Z. Chajecki, D. Coupland, H. Iwasaki, M. Kil-burn, J. Lee, W. G. Lynch, A. Sanetullaev, M. B. Tsang, J. Winkelbauer, M. Youngs, S. T. Marley, D. V. Shetty,A. H. Wuosmaa, T. K. Ghosh, and M. E. Howard,Phys. Rev. C , 051308 (2011).[3] M. Brodeur, T. Brunner, S. Ettenauer, A. Lapierre,R. Ringle, B. A. Brown, D. Lunney, and J. Dilling, Phys. Rev. Lett. , 212501 (2012).[4] A. T. Gallant, M. Brodeur, C. Andreoiu, A. Bader,A. Chaudhuri, U. Chowdhury, A. Grossheim, R. Klawit-ter, A. A. Kwiatkowski, K. G. Leach, A. Lennarz,T. D. Macdonald, B. E. Schultz, J. Lassen, H. Heggen,S. Raeder, A. Teigelh¨ofer, B. A. Brown, A. Magilligan,J. D. Holt, J. Men´endez, J. Simonis, A. Schwenk, andJ. Dilling, Phys. Rev. Lett. , 082501 (2014).[5] A. Kankainen, L. Canete, T. Eronen, J. Hakala,A. Jokinen, J. Koponen, I. D. Moore, D. Nesterenko,J. Reinikainen, S. Rinta-Antila, A. Voss, and J. ¨Ayst¨o,Phys. Rev. C , 041304 (2016).[6] A. Kankainen, T. Eronen, D. Gorelov, J. Hakala,A. Jokinen, V. S. Kolhinen, M. Reponen, J. Rissa-nen, A. Saastamoinen, V. Sonnenschein, and J. ¨Ayst¨o,Phys. Rev. C , 052501 (2010).[7] A. A. Kwiatkowski, B. R. Barquest, G. Bollen, C. M.Campbell, D. L. Lincoln, D. J. Morrissey, G. K.Pang, A. M. Prinke, J. Savory, S. Schwarz, C. M.Folden, D. Melconian, S. K. L. Sjue, and M. Block,Phys. Rev. C , 051302 (2009).[8] C. Yazidjian, G. Audi, D. Beck, K. Blaum, S. George,C. Gu´enaut, F. Herfurth, A. Herlert, A. Keller-bauer, H.-J. Kluge, D. Lunney, and L. Schweikhard,Phys. Rev. C , 024308 (2007).[9] M. MacCormick and G. Audi,Nucl. Phys. A , 61 (2014).[10] M. MacCormick and G. Audi,Nucl. Phys. A , 296 (2014).[11] J. Su, W. Liu, N. Zhang, Y. Shen, Y. Lam, N. Smirnova,M. MacCormick, J. Wang, L. Jing, Z. Li, Y. Wang,B. Guo, S. Yan, Y. Li, S. Zeng, G. Lian, X. Du, L. Gan,X. Bai, Z. Gao, Y. Zhang, X. Zhou, X. Tang, J. He,Y. Yang, S. Jin, P. Ma, J. Ma, M. Huang, Z. Bai, Y. Zhou,W. Ma, J. Hu, S. Xu, S. Ma, S. Chen, L. Zhang, B. Ding,Z. Li, and G. Audi, Phys. Lett. B , 323 (2016).[12] Y. H. Zhang, H. S. Xu, Y. A. Litvinov, X. L. Tu, X. L.Yan, S. Typel, K. Blaum, M. Wang, X. H. Zhou, Y. Sun,B. A. Brown, Y. J. Yuan, J. W. Xia, J. C. Yang, G. Audi,X. C. Chen, G. B. Jia, Z. G. Hu, X. W. Ma, R. S.Mao, B. Mei, P. Shuai, Z. Y. Sun, S. T. Wang, G. Q.Xiao, X. Xu, T. Yamaguchi, Y. Yamaguchi, Y. D. Zang,H. W. Zhao, T. C. Zhao, W. Zhang, and W. L. Zhan,Phys. Rev. Lett. , 102501 (2012).[13] C. Dossat, N. Adimi, F. Aksouh, F. Becker, A. Bey,B. Blank, C. Borcea, R. Borcea, A. Boston, M. Caa-mano, G. Canchel, M. Chartier, D. Cortina, S. Cza-jkowski, G. de France, F. de Oliveira Santos, A. Fleury,G. Georgiev, J. Giovinazzo, S. Grvy, R. Grzywacz,M. Hellstr¨om, M. Honma, Z. Janas, D. Karamanis,J. Kurcewicz, M. Lewitowicz, M. L. Jim´enez, C. Maz-zocchi, I. Matea, V. Maslov, P. Mayet, C. Moore,M. Pf¨utzner, M. Pravikoff, M. Stanoiu, I. Stefan, andJ. Thomas, Nucl. Phys. A , 18 (2007).[14] S. E. A. Orrigo, B. Rubio, Y. Fujita, W. Gelletly,J. Agramunt, A. Algora, P. Ascher, B. Bilgier, B. Blank,L. C´aceres, R. B. Cakirli, E. Ganio˘glu, M. Gerbaux,J. Giovinazzo, S. Gr´evy, O. Kamalou, H. C. Kozer, L. Ku-cuk, T. Kurtukian-Nieto, F. Molina, L. Popescu, A. M.Rogers, G. Susoy, C. Stodel, T. Suzuki, A. Tamii, andJ. C. Thomas, Phys. Rev. C , 044336 (2016).[15] J. Ekman, D. Rudolph, C. Fahlander, R. Charity, W. Re-viol, D. Sarantites, V. Tomov, R. Clark, M. Cromaz,P. Fallon, A. Macchiavelli, M. Carpenter, and D. Sew- eryniak, Eur. Phys. J. A , 13 (2000).[16] M. A. Bentley, S. J. Williams, D. T. Joss, C. D.O’Leary, A. M. Bruce, J. A. Cameron, M. P. Car-penter, P. Fallon, L. Frankland, W. Gelletly, C. J.Lister, G. Mart´ınez-Pinedo, A. Poves, P. H. Regan,P. Reiter, B. Rubio, J. Sanchez Solano, D. Seweryniak,C. E. Svensson, S. M. Vincent, and D. D. Warner,Phys. Rev. C , 051303 (2000).[17] G. Audi, A. Wapstra, and C. Thibault,Nucl. Phys. A , 337 (2003).[18] Y. Dong and H. Junde,Nucl. Data Sheets , 185 (2015).[19] E. Hagberg, I. Towner, J. Hardy,V. Koslowsky, G. Savard, and S. Sterbenz,Nucl. Phys. A , 183 (1997).[20] G. Audi, F. Kondev, M. Wang, B. Pfeiffer,X. Sun, J. Blachot, and M. MacCormick,Chin. Phys. C , 1157 (2012).[21] K. Jackson, C. Cardinal, H. Evans, N. Jelley, andJ. Cerny, Phys. Lett. B , 281 (1970).[22] J. Cerny, J. Esterl, R. Gough, and R. Sextro,Phys. Lett. B , 284 (1970).[23] J. Cerny, R. Gough, R. Sextro, and J. E. Esterl,Nucl. Phys. A , 666 (1972).[24] A. Kankainen, V.-V. Elomaa, T. Eronen, D. Gorelov,J. Hakala, A. Jokinen, T. Kessler, V. S. Kolhinen,I. D. Moore, S. Rahaman, M. Reponen, J. Rissa-nen, A. Saastamoinen, C. Weber, and J. ¨Ayst¨o,Phys. Rev. C , 034311 (2010).[25] R. K. Wallace and S. E. Woosley,Astrophys. J. Suppl. Ser. , 389 (1981).[26] H. Schatz, A. Aprahamian, J. G¨rres, M. Wiescher,T. Rauscher, J. Rembges, F.-K. Thielemann, B. Pfeif-fer, P. M¨oller, K.-L. Kratz, H. Herndl, B. Brown, andH. Rebel, Phys. Rep. , 167 (1998).[27] A. Parikh, J. Jos´e, C. Iliadis, F. Moreno, andT. Rauscher, Phys. Rev. C , 045802 (2009).[28] I. Moore, T. Eronen, D. Gorelov, J. Hakala, A. Jokinen,A. Kankainen, V. Kolhinen, J. Koponen, H. Penttil¨a,I. Pohjalainen, M. Reponen, J. Rissanen, A. Saasta-moinen, S. Rinta-Antila, V. Sonnenschein, and J. ¨Ayst¨o,Nucl. Instrum. Meth. Phys. Res. B , 208 (2013),XVIth International Conference on ElectroMagneticIsotope Separators and Techniques Related to theirApplications, December 27, 2012 at Matsue, Japan.[29] P. Karvonen, I. Moore, T. Sonoda, T. Kessler, H. Pent-til¨a, K. Per¨aj¨arvi, P. Ronkanen, and J. ¨Ayst¨o,Nucl. Instrum. Meth. Phys. Res. B , 4794 (2008).[30] A. Nieminen, J. Huikari, A. Jokinen,J. ¨Ayst¨o, P. Campbell, and E. Cochrane,Nucl. Instrum. Meth. Phys. Res. A , 244 (2001).[31] T. Eronen, V. S. Kolhinen, V. V. Elomaa, D. Gorelov,U. Hager, J. Hakala, A. Jokinen, A. Kankainen,P. Karvonen, S. Kopecky, I. D. Moore, H. Penttil¨a,S. Rahaman, S. Rinta-Antila, J. Rissanen, A. Saas-tamoinen, J. Szerypo, C. Weber, and J. ¨Ayst¨o,Eur. Phys. J. A , 46 (2012).[32] G. Savard, S. Becker, G. Bollen, H. J. Kluge, R. B.Moore, T. Otto, L. Schweikhard, H. Stolzenberg, andU. Wiess, Phys. Lett. A , 247 (1991).[33] G. Gr¨aff, H. Kalinowsky, and J. Traut,Z. Phys. A , 35 (1980).[34] M. K¨onig, G. Bollen, H. J. Kluge, T. Otto, and J. Szerypo,Int. J. Mass Spectrom. Ion Processes , 95 (1995).[35] A. Kellerbauer, K. Blaum, G. Bollen, F. Herfurth, H.-J.Kluge, M. Kuckein, E. Sauvan, C. Scheidenberger, andL. Schweikhard, Eur. Phys. J. D , 53 (2003).[36] L. Canete, A. Kankainen, T. Eronen, D. Gorelov,J. Hakala, A. Jokinen, V. S. Kolhinen, J. Koponen,I. D. Moore, J. Reinikainen, and S. Rinta-Antila,Eur. Phys. J. A , 1 (2016).[37] C. Roux, K. Blaum, M. Block, C. Droese, S. Eliseev,M. Goncharov, F. Herfurth, M. E. Ramirez, A. D.Nesterenko, N. Y. Novikov, and L. Schweikhard,Eur. Phys. J. D , 1 (2013).[38] R. T. Birge, Phys. Rev. , 207 (1932).[39] M. Kretzschmar, Int. J. Mass Spectrom. , 122 (2007).[40] S. George, K. Blaum, F. Herfurth, A. Herlert, M. Kret-zschmar, S. Nagy, S. Schwarz, L. Schweikhard, andC. Yazidjian, Int. J. Mass Spectrom. , 110 (2007).[41] T. Eronen, V.-V. Elomaa, J. Hakala, J. C. Hardy,A. Jokinen, I. D. Moore, M. Reponen, J. Rissa-nen, A. Saastamoinen, C. Weber, and J. ¨Ayst¨o,Phys. Rev. Lett. , 252501 (2009).[42] T. Eronen, V.-V. Elomaa, U. Hager, J. Hakala,A. Jokinen, A. Kankainen, S. Rahaman,J. Rissanen, C. Weber, and J. ¨Ayst¨o,Nucl. Instrum. Meth. Phys. Res. B , 4527 (2008),Proceedings of the XVth International Conference onElectromagnetic Isotope Separators and TechniquesRelated to their Applications.[43] M. Wang, G. Audi, A. Wapstra, F. Kon-dev, M. MacCormick, X. Xu, and B. Pfeiffer,Chin. Phys. C , 1603 (2012).[44] X. Tu, Y. Litvinov, K. Blaum, B. Mei, B. Sun,Y. Sun, M. Wang, H. Xu, and Y. Zhang,Nucl. Phys. A , 89 (2016).[45] D. Rudolph, R. Hoischen, M. Hellstr¨om, S. Pietri,Z. Podoly´ak, P. H. Regan, A. B. Garnsworthy, S. J.Steer, F. Becker, P. Bednarczyk, L. C´aceres, P. Door-nenbal, J. Gerl, M. G´orska, J. Grebosz, I. Kojouharov,N. Kurz, W. Prokopowicz, H. Schaffner, H. J. Woller-sheim, L. L. Andersson, L. Atanasova, D. L. Balabanski,M. A. Bentley, A. Blazhev, C. Brandau, J. R. Brown,C. Fahlander, E. K. Johansson, and A. Jungclaus,Eur. Phys. J. A , 131 (2008).[46] H. Xiaolong, Nucl. Data Sheets , 2131 (2006).[47] D. Mueller, E. Kashy, and W. Benenson,Phys. Rev. C , 1282 (1977). [48] X. Tu, M. Wang, Y. Litvinov, Y. Zhang, H. Xu,Z. Sun, G. Audi, K. Blaum, C. Du, W. Huang, Z. Hu,P. Geng, S. Jin, L. Liu, Y. Liu, B. Mei, R. Mao,X. Ma, H. Suzuki, P. Shuai, Y. Sun, S. Tang, J. Wang,S. Wang, G. Xiao, X. Xu, J. Xia, J. Yang, R. Ye, T. Ya-maguchi, X. Yan, Y. Yuan, Y. Yamaguchi, Y. Zang,H. Zhao, T. Zhao, X. Zhang, X. Zhou, and W. Zhan,Nucl. Instrum. Meth. Phys. Res. A , 213 (2011).[49] A. Gadea, S. Lenzi, D. Napoli, M. Axiotis, C. Ur,G. Mart´ınez-Pinedo, M. G´orska, E. Roeckl, E. Cau-rier, F. Nowacki, G. de Angelis, L. Batist, R. Borcea,F. Brandolini, D. Cano-Ott, J. D¨oring, C. Fahlander,E. Farnea, H. Grawe, M. Hellstr¨om, Z. Janas, R. Kirch-ner, M. L. Commara, C. Mazzocchi, E. N´acher, C. Plet-tner, A. Pochocki, B. Rubio, K. Schmidt, R. Schwengner,J. Tain, and J. Zylicz, Phys. Lett. B , 88 (2005).[50] G. Audi, M. Wang, A. Wapstra, F. Kon-dev, M. MacCormick, X. Xu, and B. Pfeiffer,Chin. Phys. C , 1287 (2012).[51] E.Arbman and N.Svartholm, Arkiv Fys. , 1 (1956).[52] R. Kouzes, P. Kutt, D. Mueller, and R. Sherr,Nucl. Phys. A , 329 (1978).[53] P. L. Jolivette, J. D. Goss, J. A. Bieszk, R. D. Hichwa,and C. P. Browne, Phys. Rev. C , 439 (1976).[54] T. Katoh, M. Nozawa, Y. Yoshizawa, andY. Koh, J. Phys. Soc. Japan , 2140 (1960),http://dx.doi.org/10.1143/JPSJ.15.2140.[55] F. Becchetti, D. Dehnhard, and T. Dzubay,Nucl. Phys. A , 151 (1971).[56] J. Konijn, B. V. Nooijen, and H. Hagedoorn,Physica , 377 (1958).[57] G. Rickards, B. Bonner, and G. Phillips,Nucl. Phys. , 167 (1966).[58] O. Hansen, (1967), proc. 3rd Int. Conf. Atomic Massesand Fundamental Constants, p. 527.[59] A. Sperduto, (1967), proc. 3rd Int. Conf. Atomic Massesand Fundamental Constants, p. 657.[60] P. Decowski, W. Benenson, B. Brown, and H. Nann,Nucl. Phys. A , 186 (1978).[61] R. M. DelVecchio, Phys. Rev. C , 677 (1973).[62] S. Naimi, G. Audi, D. Beck, K. Blaum, C. B¨ohm,C. Borgmann, M. Breitenfeldt, S. George, F. Her-furth, A. Herlert, A. Kellerbauer, M. Kowalska, D. Lun-ney, E. Minaya Ramirez, D. Neidherr, M. Rosen-busch, L. Schweikhard, R. N. Wolf, and K. Zuber,Phys. Rev. C86