Excitation energy and angular momentum dependence of the nuclear level density parameter around A ≈ 110
Pratap Roy, S. Mukhopadhyay, Mamta Aggarwal, Deepak Pandit, T. K. Rana, Samir Kundu, T. K. Ghosh, K. Banerjee, G. Mukherjee, S. Manna, A. Sen, R. Pandey, Debasish Mondal, S. Pal, D. Paul, K. Atreya, C. Bhattacharya
aa r X i v : . [ nu c l - e x ] D ec Excitation energy and angular momentum dependence of the nuclear leveldensity parameter around A ≈ Pratap Roy , ∗ , S. Mukhopadhyay , , Mamta Aggarwal , Deepak Pandit , , T. K. Rana , ,Samir Kundu , , T. K. Ghosh , , K. Banerjee , , G. Mukherjee , , S. Manna , , A. Sen , ,R. Pandey , Debasish Mondal , S. Pal , D. Paul , , K. Atreya , , and C. Bhattacharya , Variable Energy Cyclotron Centre, 1/AF, Bidhan Nagar, Kolkata - 700064, India Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai - 400094, India Department of Physics, University of Mumbai, Kalina Campus, Mumbai-400098, India(Dated: December 8, 2020)Neutron kinetic energy spectra in coincidence with low-energy γ -ray multiplicities have beenmeasured around A ≈
110 in the O, Ne + Nb reactions in a compound nuclear excitationenergy range of ≈
90 - 140 MeV. The excitation energy (temperature) and angular momentum(spin) dependence of the inverse level density parameter k has been investigated by comparingthe experimental data with statistical Hauser-Feshbach calculation. In contrast to the availablesystematic in this mass region, the inverse level density parameter showed an appreciable increaseas a function of the excitation energy. The extracted k -values at different angular momentumregions, corresponding to different γ -multiplicities also showed an overall increase with the averagenuclear spins. The experimental results have been compared with a microscopic statistical-modelcalculation and found to be in reasonable agreement with the data. The results provide usefulinformation to understand the variation of nuclear level density at high temperature and spins. PACS numbers:
I. INTRODUCTION
Understanding the exact nature of variation of nu-clear level density (NLD) as a function of key fac-tors such as excitation energy, angular momentum,iso-spin, shell and collective effects is of particularimportance in both nuclear structure and reactionphysics. NLD serves as the most critical input inthe statistical models used to estimate the reactioncross-sections for various processes ( e.g. thermonu-clear reactions, fission, evaporation and spallation)in the interdisciplinary areas of nuclear physics, re-actor physics and astrophysics. It also acts as a test-ing ground for different nuclear structure models aswell as provides crucial information on the thermo-dynamic properties of atomic nuclei [1–12].Theoretically, the simplest and most widely used de-scription of level density is given in terms of the non-interacting Fermi gas model (
FGM ) [13], ρ ( E ) = 112 √ σ exp 2 √ aEa / E / , (1)where E is the excitation energy and σ is the spincut-off factor. The most important parameter in the FGM description of NLD is the level density (LD)parameter a which is directly related to the densityof single-particle states near the Fermi surface. It iswell-known that at low energies, the level density is ∗ Email: [email protected] strongly influenced by shell and pairing (odd-even)effects. The pairing effect can be incorporated byshifting the excitation energy on the right-hand sideof Eq. 1 by an amount related to the pairing energy(∆) [14]. On the other hand, the shell effect can betaken care of through excitation energy-dependentparametrization of the level density parameter assuggested by Ignatyuk et al. [15], a = ˜ a [1 − ∆ SU { − exp( − γU ) } ] . (2)Here U = E − ∆, ∆ S is the ground state shell cor-rection and γ is the shell damping parameter. Theasymptotic level density parameter ˜ a , which variessmoothly with the mass number A can be repre-sented as ˜ a = A/k , where k is called the inverselevel density parameter. At high excitation ener-gies or temperatures ( T & a ≈ ˜ a . The angular mo-mentum dependence of NLD described within theFermi gas picture is given by the Gaussian functionexp( − ( J +1 / σ ), where the width of the Gaussian isdetermined by the temperature ( T ) dependent spincut-off factor σ (= IT ~ where I is the moment of in-ertia).In the level density formulations based on the sim-plistic FGM , the level density parameter does notexplicitly depend on the excitation energy or angu-lar momentum. However, a number of earlier studieshave shown that the parameter k (and thus a ) de-pends on excitation energy (temperature) [16–34],and angular momentum [35–42] both, in an intricatemanner. Such departures from the FGM may notbe surprising as the actual single-particle spectrumof a nucleus is considerably complicated than thesimple Fermi gas picture. The experimental data onthe spin and excitation-energy dependence of leveldensity thus provide crucial information on the un-derlying nuclear structure and offer a stringent testfor nuclear models.Experimentally, nuclear level density can be com-puted by different techniques such as the directcounting of nuclear levels [43–46], analysis of neu-tron resonance spacings [47] and measurement ofprimary γ -ray spectra [48]. However, all these meth-ods are limited to low excitation energies and spins.The major source of knowledge about level densitiesat higher excitation energies and spins comes fromthe statistical model analysis of particle-evaporationspectra in heavy-ion fusion reactions [17–30].The analyses of the light-particle evaporation spec-tra for several medium and heavy nuclei ( A > k ( U ) = k + κ × ( U/A ) , (3)where k is the value of k at U or T = 0. The reduc-tion of the level density parameter (an increase of k ) at higher energies is consistent with the expectedfadeout of long-range correlations at higher temper-atures. However, the situation for lighter systemshas been rather complex since many studies havereported very weak, or no dependence of k on en-ergy [27–29]. Subsequently, it has been realized thatthe energy dependence of the LD parameter may de-pend on the nuclear mass number that can be takencare of by the A dependence of the parameter κ (willbe called the rate parameter hereafter). Based onthe available experimental data a mass number de-pendent parametrization of κ has been suggested byR. J. Charity [17] κ = 0 . . A ) . (4)However, such a strong mass dependence of the rateparameter is unexpected, and not supported by the-oretical calculations [31, 32]. Because of the sug-gested A dependence in Eq. 4, the resultant valueof κ is minimal for systems with A <
150 providinglittle dependence of k on energy.It should be emphasized here, that experimentaldata for lighter systems are quite limited, and theuncertainties in the extracted κ -values are large inthis mass region (see e.g. Fig. 9 of Ref. [17]). More-over, light nuclei have additional complications be-cause of the strong spin dependence of yrast energy( E yrast ). This can cause pronounced effects partic-ularly on the predicted spectra of α particles which can remove appreciable amount of angular momen-tum from the decaying system [17]. Such effectscould be much less for neutrons as they tend to re-move very little angular momentum and thus areless sensitive to E yrast . However, there is a scarcityof experimental neutron data for lighter nuclei in awide excitation energy range, and it is demandingto carry out such measurements to understand theexcitation energy dependence of the level density pa-rameter in a consistent manner.The level density parameters obtained from theexclusive particle evaporation measurements are av-erage quantities over a range of excitation energiesand angular momenta. Angular momentum gatedevaporation studies can provide information on theLD parameter at different angular momentum re-gions. However, the number of such studies arehighly limited and, the value of a particularly athigh angular momentum is practically unknown fora large number of nuclei. A few attempts have beenmade in recent years to understand the spin depen-dence of the level density parameter. Some of thesestudies showed interesting variations of the LD pa-rameter as a function of angular momentum ( J ). Asystematic reduction of k with increasing
10 - 20 ~ have been reported in therecent neutron evaporation studies around A ≈
90 -120 [38–40]. On the other hand, angular momentumgated α -particle evaporation measurement around A ≈ J ≈
10 - 20 ~ showed complex vari-ation of k with angular momentum [37]. In con-trast to the strong dependence of the LD parame-ter on the angular momentum reported in the abovementioned works, experimental data for the heaviersystems showed less sensitivity of k on J [35, 36].Some of the experimental data on the angular de-pendence of k could be successfully explained by thetheoretical calculations by considering spin induceddeformation and shape phase transitions under theframework of a statistical theory of hot rotating nu-clei [41, 42]. In view of the observed variation of thelevel density parameter with J in the earlier works,it will be interesting to extend the study for similarsystems especially to higher spin regions.With the motivations described above we havemeasured γ -ray multiplicity gated neutron evapo-ration spectra from In ( O + Nb) and
Sb( Ne + Nb) compound systems. In this paper,we report the average variation of the (inverse) leveldensity parameter as a function of the excitation en-ergy (temperature) and angular momentum for thenuclei around A ≈
110 in the range of T ≈
20 - 36 ~ . The experimental re-sults have been compared with the theoretical cal-culations performed with a statistical theory of hotrotating nuclei. The present study is expected toprovide useful information in understanding the na- (cid:1)(cid:0)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6) (cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:13)(cid:14)(cid:15) (cid:16)(cid:17)(cid:18)(cid:19) (cid:20)(cid:21)(cid:22)(cid:23)(cid:24) (cid:25)(cid:26)(cid:27)(cid:28) (cid:29)(cid:30)(cid:31) FIG. 1: (Color online) Schematic representation of theexperimental setup. ture of level density at high temperature and spins.The article has been arranged in the followingmanner. The experimental arrangement has beendescribed in Sec. II. The results have been presentedand discussed in Sec. III; the excitation energy andtemperature dependence of the LD parameter hasbeen presented in Sec. III A, and the angular mo-mentum dependence is discussed in Sec. III B. Sec-tion III C gives a brief description of the microscopicMSM calculation. Finally, the present work is sum-marized in Sec. IV.
II. EXPERIMENTAL DETAILS
The experiment was performed using O( E lab = 116, 142 and 160 MeV) and Ne( E lab = 145 and 180 MeV) ion-beams fromthe K130 cyclotron at VECC, Kolkata. A self-supporting foil of Nb (thickness ≈ )was used as the target. The compound nuclei In and
Sb were populated in the excitationenergy range of E ∗ CN ≈
90 - 140 MeV. The neutronsemitted during the compound nuclear decay processwere detected using eight liquid scintillator basedneutron detectors (size: 5-inch × lab ) of 45 ◦ , 60 ◦ , 75 ◦ , 90 ◦ ,105 ◦ , 120 ◦ , 135 ◦ and 150 ◦ at a distance of 2 mfrom the target. A schematic of the experimentalsetup used in the present measurement is shown inFig 1. The neutron kinetic energies were measuredusing the time-of-flight (TOF) technique. The starttrigger for the TOF measurement was generatedby detecting the low-energy γ -rays in a 50-elementBaF detector array [49] placed near the targetposition. In converting the neutron TOF to neutronenergy, the prompt γ peak in TOF spectrum wasused as the time reference. The neutron and γ separation was achieved by using both the TOFand pulse shape discrimination methods [50]. The energy-dependent detection efficiency of the neutrondetectors were obtained using the Monte Carlo code NEFF [51]. The detector efficiency at low energies(1 - 10 MeV) was also measured experimentallyusing a
Cf source and found to be in goodagreement with the
NEFF calculation [52].The multiplicity of the low-energy γ rays was alsomeasured using the BaF detector array. The arraywas split into two blocks of 25 detectors each andwas placed on the top and bottom of the thin wall( ≈ γ rays of different folds ( F ) which is defined as thenumber of BaF detectors fired simultaneously in anevent, and directly related to the populated angularmomentum. The angular momentum distributionsfor different folds were obtained by convertingthe measured γ -fold distribution using the MonteCarlo simulation technique based on the GEANT3 toolkit, by including real experimental conditionslike detector threshold and trigger conditions in thesimulation [49].To keep the background of the neutron detectors atminimum level [53], the beam dump was kept at adistance of ≈ III. RESULTS AND DISCUSSIONS
The background-corrected neutron spectra mea-sured at various laboratory angles were transformedinto the compound nucleus (CN) center-of-mass(c.m.) frame using the standard Jacobian transfor-mation. The neutron spectra in the c.m. framemeasured at different angles at the highest bom-barding energies have been shown in Fig. 2. Theexperimental spectra have been compared with thestatistical Hauser-Feshbach (HF) calculation (shownby the dashed lines in Fig. 2) performed using the
CASCADE computer code [54]. For the level den-sity, the Reisdorf [55] prescription as presented inRef. [56] has been used. ρ ( E, J ) = 2 J + 112 θ / √ a e xp (2 √ aU ) U (5)where U = E − J ( J + 1) θ − ∆ (6) E c.m. (MeV) d s / d W d E ( a r b . un it s ) E c.m. (MeV) E lab = 160 MeV O + Nb(a) E lab = 180 MeV Ne + Nb(b)
FIG. 2: (Color online) Experimental inclusive neutronspectra at different angles (symbols) in the c.m. frame(a) for the O + Nb reaction at E lab = 160 MeVand (b) for the Ne + Nb at E lab = 180 MeV. Thelines are the prediction of statistical HF calculation. Theindividual spectrum at different angles has been scaledfor better visualization. Here ∆ is the pairing correction which was taken as∆ = δ (12 / √ A ), where δ = -1, 0 and 1 for odd-odd,even-odd and even-even nuclei, respectively. Here θ = I eff ~ ; the effective moment of inertia I eff isrelated to the rigid body moment of inertia ( I ) as I eff = I (1 + δ J + δ J ) [57]. The quantities δ and δ known as the deformability coefficients areadjustable input parameters providing a range ofchoices for the spin dependence of the level density.The default values of δ and δ are obtained usingthe rotating liquid drop model [58]. The shell effectin NLD has been incorporated by using Eq. 2;the smoothly varying (asymptotic) level densityparameter in Eq. 2 was estimated as ˜ a = A/k where k has been treated as a free parameter. Thetransmission coefficients were calculated using theoptical model (OM), where the OM parameterswere taken from Ref. [59]. It was observed thatthe variation in the OM parameters as well as thedeformability coefficients had no significant effecton the shape of the calculated neutron evaporationspectra which were mainly decided by the valueof the LD parameter. The inverse level densityparameter k has been tuned to obtain the bestmatch to the experimental spectra.It can be seen from Fig. 2 that the spectral shapesat the backward angles are almost overlapping,and they agree very well with the statistical modelpredictions even at the highest incident energies.This indicates that for the present bombardingenergies (7 - 10 MeV/ A ) the spectra at back anglesare mostly determined by the compound nuclear U (MeV)
50 60 70 80 90 100 110 k ( M e V ) Data ( O + Nb)Data ( Ne + Nb)Eq. 3
FIG. 3: (Color online) The excitation energy dependenceof the inverse level density parameter k . emission process and any contribution comingfrom the non-equilibrium processes are small. Theexistence of the non-equilibrium component isevident in the high-energy tails of the spectra atthe forward angles (Fig. 2). It is interesting to notethat qualitatively the non-equilibrium contributionsseems to be more for the O + Nb reactionthan the Ne + Nb reaction at similar incidentenergies.In the present bombarding energy range the spectraat the most backward angle (150 ◦ ) is consideredalmost free of the non-equilibrium component, andwas used for further analysis to understand theexcitation energy and spin dependence of the leveldensity parameter. A. Excitation energy and temperaturedependence of k The back-angle inclusive neutron energy spectrafor the O and Ne + Nb reactions at differ-ent excitation energies were fitted with
CASCADE predictions by varying the inverse level density pa-rameter k . The optimum values of k correspondingto different excitation energies were extracted by fit-ting the experimental neutron spectra using the χ minimization technique. The extracted k -values asa function of the thermal excitation energy ( U ) hasbeen plotted in Fig. 3. The thermal excitation en-ergy corresponding to the first stage of the the decay( i.e. after the emission of one neutron) has been es-timated from the following relation U = E ∗ CN − < E rot > − S n − < E n > (7)where < E rot > is mean value of the rotational en-ergy for a given E ∗ CN , S n is the neutron separation Mass number (A)
100 150 200 k -1 Ref. [17]Ref. [60]Ref. [16]Present workRef . [32]Eqn. 4 FIG. 4: (Color online) The values of κ as a function ofthe mass number. The present data is shown by thesquare. The filled circles and the arrows are regeneratedfrom Ref. [17]. The filled triangles are obtained fromthe energy dependence of k provided in Ref. [60]. Thered-continuous line shows the prediction of Eq. 4. Thepink-dashed curve shows the κ values extracted from thetheoretical predictions of Ref. [32]. energy and
FIG. 5: (Color online) The temperature dependence ofthe inverse level density parameter. The experimentaldata are shown by the symbols. The dashed line showsthe prediction of Ref. [32] reduced by a factor of 1.25. cade. However, the measured neutron spectra con-tain contributions coming from different stages ofthe decay. Therefore, it is appropriate to describethe system with an average temperature which issomewhat lower than the one given by Eq. 8. The av-erage or apparent temperatures ( T av ) correspondingto the different excitation energies were obtained byfitting the experimental spectra with the Maxwellianfunction √ E n exp ( − E n /T av ). The experimental re-sult on the temperature dependence of k (shown bythe symbols in Fig. 5) has been compared with theavailable theoretical calculation of Shlomo and Na-towitz [32] performed under the Thomas-Fermi ap-proach for a nucleus with A = 110. It should benoted that the calculation of Ref. [32] somewhatover-predicts the absolute values of k obtained inthe present work. Therefore, in order to make ameaningful comparison with the data the calculatedvalues of Ref. [32] were scaled down (reduced) bya constant factor of 1.25. It can be observed fromFig. 5 that the observed temperature dependenceagrees nicely with the predicted trend of Ref. [32]after the reduction (dashed line in Fig. 5). It maybe mentioned here that the reduction in the valueof the level density parameter (the increase of k )with temperature can mainly be accounted for, bythe temperature dependence of the frequency andmomentum dependent effective mass [32]. The fre-quency dependence of the effective mass, which re-flects the effects of correlations, considerably en-hances the surface contribution to a at low ener-gies [61]. However, the effect of correlation dies outwith the increase in excitation energy, reducing thevalue of the level density parameter at higher tem-peratures. E c.m. (MeV) d N / d E ( c oun t s / M e V ) F2F3F4F5F6F7F8&m E c.m. (MeV) F2F3F4F5F6F7F8&m E c.m. (MeV) F2 F3F4F5F6F7F8&m E lab = 116 MeV O + Nb E lab = 160 MeV O + Nb E lab = 145 MeV Ne + Nb(a) (b) (c)
FIG. 6: (Color online) Experimental neutron spectra (symbols) at different folds for the O + Nb reaction at theincident energies of (a) 116 MeV and (b) 160 MeV, and (c) for the Ne + Nb at E lab = 145 MeV. The lines arethe prediction of statistical HF calculation. The individual spectrum at at different folds has been scaled for bettervisualization. B. Angular momentum dependence of k The experimental neutron energy spectra for dif-ferent γ -folds ( F ), corresponding to different an-gular momentum regions were extracted and com-pared with the theoretical CASCADE calculationsas shown in Fig. 6. As mentioned, the angular mo-mentum distributions corresponding to different γ -folds have been extracted by using the GEANT3 based simulation technique described in Ref. [49] indetail. The theoretical neutron energy spectra werecalculated using
CASCADE , with the extracted an-gular momentum distributions for different folds asinputs. The best-fit values of the inverse level den-sity parameter as obtained from the theoretical fitsto the neutron spectra, for different folds, are givenin Table I.The k -values as a function of the mean angular mo-mentum in the daughter nuclei have been plotted inFig. 7. It is observed that the experimental k -valuesincreases as a function of the mean angular momen-tum for both the O + Nb and Ne + Nb reac-tions in the measured angular momentum range of
20 - 36 ~ . The experimental results havebeen compared with the microscopic calculationsperformed using the statistical model of hot rotatingnuclei [41, 42, 62], described briefly in the followingsection (Sec. III C). It should be mentioned that theexperimental neutron spectra contain contributionscoming from the different stages of the decay leadingto different residual nuclei. Therefore, the extracted level density parameters do not strictly correspondto any specific daughter nucleus, rather they repre-sent the average value for nuclei in the given massregion. In order to compare with the experimen-tal data the theoretical calculations were performedfor the three most significant daughter nuclei corre-sponding to the 1 n , 2 n and αn decay channels ( i.e. In,
In and
Ag for the O + Nb reactionand
Sb,
Sb and
In for the Ne + Nb re-action). The outcome of this calculation has beenshown by the line plus symbol plots in Fig. 7. Theexperimental data on the average agree reasonablywell with the predicted values.
C. Microscopic calculation and comparisonwith the data
To investigate the observed energy and angularmomentum dependence of the level density parame-ter theoretically, a microscopic calculation has beenperformed within the theoretical framework thatinvolves the statistical theory [41, 42, 42, 63], andthe Macroscopic-Microscopic approach using the tri-axially deformed Nilsson-Strutinsky model [64, 65].In this model, the excited compound nuclei are de-scribed as the thermodynamical system of fermionsincorporating their collective and non-collectiverotational degrees of freedom. The basic ingredient
TABLE I: Average angular momenta in the residual nu-clei and the extracted inverse level density parametersfor different γ -folds.System E lab Fold < J > ( k )(CN) ( E ∗ CN ) ( ~ ) (MeV)(MeV) 2 20.9 8.1 ± ± O+ Nb 116 4 26.0 8.6 ± ± In) (93.5) 6 29.2 8.9 ± ± ≥ ± ± ± O+ Nb 160 4 26.4 8.7 ± ± In) (131.0) 6 29.6 9.5 ± ± ≥ ± ± ± Ne+ Nb 145 4 29.0 7.8 ± ± Sb) (109.5) 6 32.3 8.1 ± ± ≥ ± of the theory is a suitable shell-model level schemefor various deformations, which is generated byassuming that the nucleons move in a deformedoscillator potential of the Nilsson Hamiltonian,diagonalized with cylindrical basis states [66, 67]with the Hill-Wheeler [68] deformation parameters.The levels up to N = 11 shells of the Nilsson modelwith Seeger parameters [69] are used.The equilibrium deformation ( β ) and shape ( γ ) ofthe nucleus have been determined by minimizingthe appropriate free energy F = E − T S [70]. Theminima of F have been traced with respect tothe intrinsic shape parameters β and γ which alsodescribe the orientation of the nucleus with respectto its rotation axis. The total energy ( E ) andentropy ( S ) which are functions of particle number,deformation and shape alongwith the orientationwith respect to rotation axis are computed withinthis microscopic statistical model (MSM).Having the single-particle ( s.p. ) level scheme,the occupation probabilities of these s.p. levelsare calculated at different temperatures ( T ) byfollowing the Fermi distribution function. Thecorresponding excitation energies ( U ) are thenextracted by adding the single-particle energiesof the occupied levels and subtracting the groundstate energy from it [42, 62]. Subsequently, the leveldensity parameter is obtained by using the Fermi
20 22 24 26 28 30 32 34 k ( M e V ) Expt. data In In Ag
20 22 24 26 28 30 32 34 k ( M e V ) Expt. data In In Ag Ne + Nb
22 24 26 28 30 32 34 36 38 k ( M e V ) Expt. data Sb Sb In (a)(b)(c) O + Nb O + Nb FIG. 7: (Color online) The experimental k -values (sym-bols) as a function of average angular momenta for the O + Nb reaction at the compound nuclear excita-tion energy ( E ∗ CN ) of (a) 93.5 and (b) 131 MeV, and (c)for the Ne + Nb reaction at E ∗ CN =109.5 MeV. Theline+symbol plots represent the theoretical predictionsfor the three most significant daughter nuclei obtainedwithin the statistical model of hot-rotating nuclei (seethe text). gas formula a = U/T , and the inverse level densityparameter k is evaluated as k = A/a . The totallevel density ( ρ ) has been calculated using Eq. 5with the MSM computed level density parameters.The microscopic model used in the present workhave been adequately described in Refs. [42, 62, 65],and the reader may refer to these articles for thedetails of the formalism.The nuclear level density, the temperature de- (a) U (MeV)
20 40 60 80 r ( M e V - ) In In Ag Sb Sb (b) T (MeV) U ( M e V ) In In Ag Sb Sb (c) T (MeV) k ( M e V ) In In Ag Sb Sb FIG. 8: (Color online) The theoretical results for dif-ferent nuclei obtained within the microscopic statisticalmodel (see the text). (a) The energy dependence of thetotal level density. The temperature dependence of the(b) thermal energy and (c) the inverse level density pa-rameter. pendence of excitation energy and the inverse LDparameter obtained from the MSM calculation forthe residual nuclei
In,
In,
Ag,
Sb and
Sb in the excitation energy range covered exper-imentally in the present work are shown in Fig. 8.The excitation energy increases with temperatureapproximately as the Fermi gas relation U = aT (Fig. 8(b)). The shell effects are prominent atlow T , which is visible in the fluctuations in the k values, as shown in Fig. 8(c). After the shelleffects get quenched ( for T & k increases smoothly withtemperature for all the systems (Fig. 8(c)); the trend agrees reasonably with the average variationof k observed in the present experimental data asshown in Fig. 5. The predicted results also matchwith the trend shown in Refs. [32, 71, 72]. Thenuclear level density ρ ( U ) as shown in Fig. 8(a)increases rapidly with U (and T ) and eventuallyslows down at higher energies where k increaseswith temperature.The angular momentum dependence of k has alsobeen investigated within the MSM. The k -valuesat a given initial temperature corresponding to theexperimental excitation energies for the differentsystems have been evaluated at different angularmomenta in the range of J = 20 - 40 ~ . The resultsare shown in Fig. 7 for the different daughter nuclei.The predicted angular momentum dependence forthe nuclei under consideration matches with theaverage variation of k with
The neutron kinetic energy spectra emitted fromthe excited
In and
Sb compound systemshave been measured in the excitation energy rangeof E ∗ CN ≈
90 - 140 MeV. The multiplicity oflow-energy γ rays was also measured to estimatethe populated angular momentum. The theoreticalanalysis of the neutron spectra was performedwithin the statistical Hauser-Feshbach formalismto investigate the excitation energy (temperature)and angular momentum dependence of the leveldensity parameter for the nuclei around A = 110.The experimental data clearly show that the leveldensity parameter a decreases with the increase inexcitation energy (temperature) as well as angularmomentum. The energy dependence of the leveldensity parameter for the present systems could beexpressed as ˜ a ( U ) = A . . U/A ) . The observedvariation of the LD parameter is in contrast to theavailable systematic in this mass region; however,the trend matches nicely with the theoreticalcalculations. It would be interesting to carry outfurther experimental investigations in this massregion to get a more comprehensive picture of theobserved phenomenon.The angular momentum dependence of a has beeninvestigated from the analysis of γ -ray multiplicitygated neutron spectra, and it is observed that fora given initial temperature, the k -values increasewith
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