Small Quadrupole Deformation for the Dipole Bands in {}^{112}In

Small Quadrupole Deformation for the Dipole Bands in In

T. Trivedi    R. Palit    J. Sethi    S. Saha    S. Kumar    Z. Naik    V. V. Parkar111Present address: Departamento de Física Aplicada, Universidad de Huelva, E-21071 Huelva, Spain    B.S. Naidu    A.Y. Deo    A. Raghav    P. K. Joshi    H. C. Jain    S. Sihotra    D. Mehta    A. K. Jain    D. Choudhury    D. Negi    S. Roy    S. Chattopadhyay    A.K. Singh    P. Singh    D.C. Biswas    R.K. Bhowmik    S. Muralithar    R. P. Singh    R. Kumar    K. Rani Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Mumbai - 400005, INDIA Department of Physics and Astrophysics, University of Delhi, Delhi-110007, INDIA Department of Physics, Panjab University, Chandigarh - 160014, INDIA Department of Physics, Indian Institute of Technology, Roorkee - 247667, INDIA Inter University Accelerator Centre, New Delhi-110067, INDIA Saha Institute of Nuclear Physics, I/AF, Bidhannagar, Kolkata - 700064, INDIA Department of Physics Meteorology, Indian Institute of Technology Kharagpur, Kharagpur - 721302, INDIA Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai - 400085, INDIA

High spin states in In were investigated using Mo(O, p3n) reaction at 80 MeV. The excited level have been observed up to 5.6 MeV excitation energy and spin 20 with the level scheme showing three dipole bands. The polarization and lifetime measurements were carried out for the dipole bands. Tilted axis cranking model calculations were performed for different quasi-particle configurations of this doubly odd nucleus. Comparison of the calculations of the model with the B(M1) transition strengths of the positive and negative parity bands firmly established their configurations.

21.10.Hw, 21.60.Jz, 25.70.Gh, 27.60.+j, 29.30.Kv

I Introduction

Various nuclear excitation modes have been understood by considering the symmetry of nuclear mean field and relative orientation of the total angular momentum with respect to its principal axes. In particular, the investigation of generation of high angular momentum states in nuclei based on symmetry consideration and geometrical models has been extremely successful in case of novel excitation modes like magnetic, anti-magnetic and chiral rotations frau (). Studies of high spin states in Ag, Cd and In near isotopes continue to reveal new aspects of these modes of excitations in nuclei si03 (); zh01 (); da05 (); ch10 (); ro11 (). Magnetic rotational (MR) bands were reported in In isotopes ch01 () and recently, two dipole bands observed in In isotope were explained in terms of different K values with same quasiparticle orbitals de09 (); pa10 (). The nuclei in this region exhibit many exciting features involving regular band structures arising from the occupancy of the valance protons and neutrons in g and h orbitals, respectively. Such high- orbitals are now well known for generation of rotation like sequences of M1 transitions called shears bands rmc (). Another interesting aspect of nuclei in this mass region is the appearance of doublet bands 104Rh (); prm (); ko10 () with same parity, which are nearly degenerate. In this picture, the degenerate bands observed in the lab-frame arise in nuclei due to the possibility of forming mutually perpendicular coupling of three angular momenta of the collective triaxial core, valence neutron and proton either in left or right handed system in the intrinsic frame of the nucleus. Relativistic Mean Field (RMF) calculations have been reported for the odd-odd nuclides in the mass region me06 (). Favorable deformation required for chirality has been predicted in Rh, Ag, and In odd-odd isotopes. These triaxial doubly odd isotopes are predicted to have multiple chiral bands. Recently, In has attracted considerable experimental attention and an elaborate level scheme of In has been reported in Ref he10 () based on Li + Pd reaction. One of the motivation of the present work is to assign the parity of different dipole bands through polarization measurements for detailed understanding of their configurations. In addition, a heavier ion beam was chosen to populate excited levels of In with higher recoil velocity required for lifetime measurements using Doppler-shift attenuation method (DSAM). The results of polarization and lifetime measurements have been used along with tilted axis cranking (TAC) calculations frau93 (); ne10 () to obtain the shape parameters and quasiparticle configurations for different bands in In. The present experimental details and results are discussed in section II and III.

Figure 1: Partial level scheme of In relevant for the present work. The -rays energies are in keV.
Figure 2: Double gated spectrum with 319 and 261-keV transitions indicating all the dipole transitions of Band A.
Figure 3: Double gated spectra obtained by (a) gates on 187 and 297-keV, and (b) 187 and 437-keV transitions. -rays transitions associated with In are labeled with their energies in keV.
Figure 4: Double gated spectra obtained by (a) gates on 588 and 297-keV, and (b) 588 and 437-keV transitions. -rays transitions associated with In are labeled with their energies in keV.

Ii Experimental Details and Analysis Procedure

High spin states in In were populated using Mo(O, p3n) reaction. The 80-MeV O beam was obtained from 15-UD Pelletron accelerator at IUAC, New Delhi. The target consisted of 2.7 mg/cm Mo with backing of 12 mg/cm Pb to stop the recoiling ions produced in the reaction. Indian National Gamma Array (INGA) consisting of eighteen Compton suppressed clover detectors was used to detect -rays emitted in the reaction. This collaborative research facility was initiated by Tata Institute of Fundamental Research, IUAC, Bhabha Atomic Research Centre, Saha Institute of Nuclear Physics, Variable Energy Cyclotron Centre, UGC-DAE-Consortium for Scientific Research, and many Universities in India. The clover detectors were arranged in five rings, at 32, 57, 90, 123, and 148 with respect to the beam direction mu10 (); bh01 (). The data were acquired when at least three clover detectors fired simultaneously. Ba and Eu radioactive sources were used for the energy calibration and determination of relative photopeak efficiency of the array. After gain matching of individual crystals, add-back spectra were generated for all the clovers and the coincidence data was stored in the matrix which has about events in total. An cube was also constructed from the data. The RADWARE software package rad95 () was used for the analysis of these matrices and the cube. The partial level scheme of In is shown in Fig. 1. Various gated spectra relevant for identifying transitions in bands A, B and C are shown in Figs. [2-4]. The double gated spectrum obtained in coincidence with 319 and 261 keV transitions shown in Fig.2 depicts the 128 - 178 - 273 - 393 - 554 - 708-keV cascade of band A. Similarly, the four double gated spectra given in Fig.3 and 4 with gate on 187-297 keV, 187 - 437 keV, 588 - 297 keV and 588 - 437 keV transition-pairs show the -rays of bands B and C as given in Refs.he10 (); he09 ().

Figure 5: Plot for DCO ratios of different transitions.
Figure 6: Plot for polarization asymmetry for different transitions.
Figure 7: (Color online) 261-keV gated spectra of the perpendicular and parallel Compton scattering in the clover detectors corresponding to (a) 319-keV, (b) 1445-keV, (c) 273-keV, and (d) 393-keV transitions. Higher counts for 273, 319 and 393-keV transitions in parallel scattered spectrum indicates their magnetic character, while (d) suggests electric nature for 1445-keV transition. An offset of 4 keV has been introduced between the parallel and perpendicular spectra for clarity.
(keV) (keV)
614 263.1 1.17(10)
670 319.2 104.3(8) 1.06(7) -0.079(28)
801 187.1
1389 588.2 134.8(9) 0.96(7) -0.037(23)
1755 1084.8 13.1(1) 1.22(10) -0.095(59)
1404.0 29.1(13) 1.96(15) 0.079(33)
2113 724.3 100(6) 1.02(6) -0.057(25)
1312.5 24.8(4) 1.69(14) 0.235(42)
2115 1445.2 75.1(4) 1.69(12) 0.058(27)
360.4 6.1(1) 1.21(11)
2493 1104.2 17.2(2) 1.16(9) -0.015(48)
2666 552.4 59.4(4) 1.02(6) -0.099(42)
1276.7 19.6(2) 1.85(18) 0.157(73)
2802 686.9 53.9(3) 1.03(7) -0.078(27)
1047.4 9.1(1) 1.78(13) 0.116(42)
3062 260.6 56.9(2) 0.97(7) -0.030(38)
947.4 4.2(2)
949.1 6.8(3)
3103 437.1 35.6(3) 0.98(6) -0.013(43)
3127 461.4 30.3(2) 0.80(5) -0.127(30)
3153 660.2 11.7(3) 0.94(9) -0.047(46)
487.7 2.2(1)
3191 128.3 60.1(2) 1.21(13)
3262 159.6 26.7(2) 0.97(9)
135.3 6.1(1) 1.09(11)
3348 194.2 10.8(1) 0.99(9)
681.9 12.1(2) 0.95(6)
3369 178.5 59.3(2) 1.06(9)
3607 344.6 20.7(1) 1.01(9)
3642 272.7 47.2(2) 0.91(6) -0.090(39)
3645 296.9 17.0(2) 0.86(7) -0.039(40)
3992 347.1 10.4(1) 1.01(9)
4035 393.3 34.5(2) 1.10(7) -0.139(26)
4354 362.4 7.8(1) 0.91(7)
4395 787.9 3.8(1) 0.89(7)
4589 554.2 20.3(2) 0.89(6) -0.157(44)
4759 404.7 5.4(1) 0.74(7)
5168 409.2 3.9(1) 1.00(9)
5297 707.6 15.6(1)
5638 470.0 2.0(1) 0.92(7)
Table 1: Excitation energies, -ray energies, intensities, DCO-ratio, multipolarity, IPDCO value and initial and final state spin of the transitions of In deduced from the present work are listed. The uncertainties in the energies of -rays are 0.3 keV for intense peaks and 0.7 keV for weak peaks.

The directional correlation of oriented states (DCO) and integrated polarization direction correlation (IPDCO) analysis were carried out to determine the spin and parity of different states. The multipolarity of -rays were deduced from the angular correlation analysis Kr89 () using the method of directional correlation from oriented states ratios (DCO) of two coincident gamma rays and , given by:

In the present geometry of detectors, the DCO ratios obtained with a stretched quadrupole (dipole) gate are 0.5(1.0) and 1.0(2.0) for the pure dipole and quadrupole transitions, respectively. The DCO ratios obtained are shown in Fig. 5. The extracted DCO values were obtained with gate on strong dipole transitions.

The clover detectors at 90 were used as a Compton-polarimeter which helps in identifying the electric or magnetic nature of -rays St99 (); Pa00 (). For a Compton-polarimeter, polarization asymmetry of the transition is defined as St99 ()


where, () is the number of counts of transitions scattered perpendicular (parallel) to the reaction plane. The correction factor is a measure of the perpendicular to parallel scattering asymmetry within the crystals of clover. For the degree detectors this parameter has been found to be 0.98(1) from the analysis of decay data of the Eu radioactive source. For linear polarization measurement, two asymmetric matrices corresponding to parallel and perpendicular segments of clover detectors (with respect to the emission plane) along one axis and the coincident -rays along the another axis were constructed la05 (). Then integrated polarization direction correlation (IPDCO) analysis was carried out. A positive value of IPDCO ratio indicates an electric transition while negative value for a magnetic transition. The positive and negative asymmetry parameters of different transitions depicted in Fig. 6 indicate their electric and magnetic nature, respectively. The 261 keV gated spectra generated from parallel ( ) and perpendicular () scattering events observed in the 90 clover detectors are shown in Fig. 7. The higher counts of the 273, 319 and 393-keV transitions in the parallel scattering spectrum compared to that in perpendicular scattering spectra suggested their magnetic nature, while the reverse nature of the spectra for 1445 keV transition confirms its electric multipolarity.

For the application of Doppler-shift attenuation method, line shapes were obtained from the background-subtracted spectra projected from the two matrices consisting of events in the 148 or 32 detectors along one axis and all other detectors along the second axis, respectively. These matrices contained approximately 5.8 10 and 4.010 coincidence events, respectively. The forward and backward Doppler shifted line shapes of 273, 393 and 554-keV transitions were shown in Fig. 8. The line shape spectra were generated by putting gate on transition below the level of interest.

Figure 8: (Color online) Representative spectra (with gate on the lower transition) along with theoretically fitted line shapes for 273, 393 and 554-keV transitions in the positive-parity yrast band of In for -ray spectra at 32, and 148 with respect to the beam direction. The contaminant peaks are marked by dashed lines.

Iii Analysis Results

iii.1 DCO and Polarization measurements

The DCO values of the transitions from the higher levels are obtained with gate on 319-keV transition. The polarization asymmetry values of the 319, 1445 and 687-keV transitions confirm the positive parity for the level at 2802 keV excitation energy. The 128 - 178 - 273 - 393 - 554 - 708-keV cascade present in the 319 and 261 keV double gated spectrum shown in Fig. 2 feeds the 2802 keV level through 261-keV transition. Polarization and DCO values obtained for 261 keV transition establishes the positive parity of the band A. The polarization asymmetry for 273, 393 and 554-keV transitions are found to be negative suggesting their magnetic character. The IPDCO of low energy transitions with energy 128 and 178-keV transitions could not be extracted and assumed to be magnetic based on the systematics of dipole bands in this mass region. Further, E2/M1 multipole mixing ratio analysis Kr89 () was carried out for the dipole transitions of band A, viz, 273, 393, and 554, from their extracted values with gate on 319-keV pure transition. The measured ratios suggest that these rays have a small E2/M1 multipole mixing ratio . This along with the IPDCO measurements suggest pure M1 nature for these intraband transitions.

The transitions of bands B and C were obtained from the double gated spectra given in Figs. 3 and 4. Based on the double gated spectra obtained with 187 - 437 keV and 588 - 437 keV pair of transitions suggest placement of 160 - 345 - 788-keV cascade above the 3103 keV state with = . The transitions placed in band C are shown in Figs. 3 and 4 in the spectra obtained with 187 - 297 and 588 - 297 keV pairs. The band-head of band C was assigned a negative parity with spin due to the measured DCO and IPDCO of the 1104 and 660 keV transitions. Two more inter-band transitions between bands B and C with energy 488 and 682 keV are also observed in the gated spectrum. The 194 - 297 - 347 - 362 - 405 - 409 - 470-keV cascade was reported in he09 (). This band C has a lower yield in the present reaction compared to band A. Therefore, only the IPDCO of 297-keV transition could be extracted and found to have magnetic nature. The DCO ratio for the 194, 297, 347 and 362-keV transitions are found to be around 1.0 suggesting the for these transitions.

(keV) (ps)
Table 2: Lifetimes of the states and reduced B() strengths of transitions of In are listed.

iii.2 Lifetime measurements

Lifetimes of the states of band A and C have been measured by DSAM. In the analysis, gating transitions were below the transitions of interest. For analyzing the line shapes of different transition of In, LINESHAPE wel91 () program was used. The program takes into account the energy loss of the beam through the target and the energy loss and angular straggling of the recoils through the target and the backing. For the energy loss calculations, we have used the shell-corrected Northcliffe and Schilling stopping powers nor70 (). The value of the time step and the number of recoil histories were chosen to be 0.01 ps and 5000, respectively. In the fitting procedure, program obtains a minimization of the fit for transition quadrupole moments () for the transition of interest, transition quadrupole moments (SF) of the modeled side feeding cascade, the intensity of contaminant peaks in the region of interest and the normalizing factor to normalize the intensity of fitted transition. The best fit was obtained through the least square minimization procedures SEEK, SIMPLEX, and MIGRAD referred in wel91 ()

In band A, the Doppler-broadened line shapes were observed for the 273, 393, 554 and 708-keV transitions above I=14 state. The line shapes of these transition were obtained by putting gate on 178-keV transition. Assuming 100 side feeding into the top of band, an effective lifetime of the top-most state was estimated which was then used as an input parameter to extract the lifetimes of lower states in the cascade. The side feeding into each level of the band was considered as a cascade of five transitions having a fixed moment of inertia comparable to that of the in-band sequences. The energies of -rays and side-feeding intensities were used as input parameters for the line shape analysis. Side-feeding intensities were calculated by using an asymmetric - matrix comprising -rays detected by detectors at 90 along one axis and all other detectors along the second axis. Once the minimization was obtained by MINUITJam75 () program, the background and the contaminant peak parameters were fixed and the procedure was followed for the next lower level. After obtaining minimization for each level, a global fit was carried out, with the background and the contaminant peak parameters of all the levels kept fixed. The side feeding lifetimes were found to be faster than the level lifetimes similar to the measurements reported in nearby nuclei in this mass region ch01 (); ne10 ().

The final values of lifetimes were obtained by taking weighted averages of the results obtained from the two separate fits which were performed at 32 and 148. For each band, B(M1) values were calculated from measured lifetimes using the following relationship:


Where, E is transition energy in MeV, is partial lifetime of the transition deduced from fitted line shape of the state and is total internal conversion coefficient of the transition, respectively. These results are listed in Table II and fitting of the theoretical line shapes with the experimental data for 273, 393 and 554-keV transitions are shown in Fig. 8. The errors quoted in lifetimes does not include the systematic errors from the uncertainty in stopping power, which can be as large as 15. Similarly, line shapes for 347 and 362-keV transitions of bands C were observed. After the fitting of calculated line shapes, the lifetime of the respective states are given in Table II.

Figure 9: (Color online)Comparison of experimentally measured B(M1) transition strength as a function of spin for dipole band 3 of In, In ch01 () and band A of In.
Figure 10: (Color online) The results of TAC calculations for the positive parity band showing (a) the variation of tilt angle with rotational frequency, (b) spin (I) vs. rotational frequency, (c) B(M1) transition strength vs. spin and (d) B(M1)/B(E2) ratio vs. spin. The experimental data shown as filled circle for band A of In are plotted in (b) and (c) for comparison.
Figure 11: The results of TAC calculations and its comparison with the experimental data for negative parity band C of In.

Iv Comparison with model calculations

The positive parity dipole band with band-head excitation energy 3.062 MeV has been observed up to . Similar dipole bands have been observed in In and In with quasi-particle configuration ch01 (). Fig. 9 demonstrates the comparison of experimentally determined B(M1) transition strengths as a function of spin for dipole band of In with band 3 of In and In ch01 () having almost similar configurations. It is evident that the B(M1) strength decreases with increasing spin up to in an identical way for all three dipole bands, which confirms the similar configuration for the positive parity dipole band of In. In addition, it is to be noted that the band crossing near MeV observed in these positive parity dipole bands of In is not seen in In ch01 (); he10 (). Very recently, a positive parity dipole band with band head spin of has been assigned the same configuration in In li11 (). This band has strong transitions with unobserved cross-over E2 transitions and no signature splitting similar to the lighter odd-odd In isotopes. It will be interesting to perform lifetime measurements for the levels in this band of In to confirm the role of shear mechanism.

In the discussion that follows, the experimental data of the dipole bands (labeled as A and C) are compared with the results of TAC model calculations. The values of proton pairing gap parameter MeV and neutron pairing gap parameter MeV were used in the TAC calculations. These values are 0.6 and 0.8 times the odd and even mass difference, respectively. The chemical potentials (both proton and neutron) were chosen so that a particle number is conserved for Z = 49 and N = 63 . The values of deformation parameter and were obtained by Nilsson Strutinsky’s minimization procedure 25 (). The nature of band A, which is a positive-parity M1 band, was investigated. A quasi-particle configuration is used in tilted axis cranking calculations for the dipole band. Similar, configurations have been assigned in lighter odd-odd In isotopes and supports magnetic rotations. A minimum is found at deformation of and . The calculated and plots based on this global minima given in Fig. 10 qualitatively explains the measured data. However, the overall decreasing trend of the experimental B(M1) values in the measured range of spin is better explained by the results of the TAC calculations based on a staic deformation with and . In particular, the measured B(M1) value at lower spin () is closer to the TAC calculation based on this lower deformation. The static minima suggests almost a constant tilt angle around and a large B(M1)/B(E2) values which is in line with the non-observation of crossover E2 transitions in band A. The low deformation of these states indicates that the contribution from the core in angular momentum generation is negligible and the whole of the angular momentum generation along the band can be attributed to the shears mechanism. Similar situation have been reported for In ne10 ()and Sn jen99 ()isotopes in the literature. Moreover, the good agreement between the TAC calculations with constant tilt angle and the measured variation of excitation energy and B(M1) values with spin for the positive parity band firmly establishes magnetic rotation for positive parity band A. This positive parity band under consideration is probably one of the ideal MR band due to very low deformation of 0.08. However, the confirmation of the small deformation will require further investigation of the crossover E2 transitions and measurement of the B(E2) values. The band crossing observed at rotational frequency 0.6 MeV for In is due to lowering of the energy of configuration at higher rotational frequency. Due to increasing neutron number up to N = 63 for In, orbitals are not available near the neutron Fermi surface for this configuration to be energetically favourable which explains the absence of band crossing for the band A.

A negative parity dipole band C studied in the present work has excitation energy of 3153 keV. The 194 - 297- 347 - 362 - 404 - 409 - 470-keV cascade extended the band C up to = . The configuration has been used in TAC for comparison of the band C which gives a minimum with and . The calculated plot (Fig. 11) explains the measured values resalable well. The measured B(M1) values at are also reproduced with the results of TAC calculations. This confirms the quasi-particle configuration of band C. In future, it will be interesting to perform the recoil distance measurements (RDM) to determine the lifetime of lower states of band C for testing the prediction of higher B(M1) values at lower spin states.

V Summary

In summary, the polarization and lifetime measurements for the excited states of the previously established level scheme of In have been carried out. Out of the three dipole bands observed in the present experiment, band A is found to have positive parity, while bands B and C have negative parity. The extracted B(M1) values from the measured lifetime of the excited states of band A has a decreasing trend with increasing spin. The TAC calculations based on configuration reproduces the measured trend of B(M1) with increasing spin. This establishes the shear rotation in In for the positive parity dipole band. The TAC calculations based on quasi-particle configurations have been compared with the measurements for band C. The fair agreement of TAC calculations with the measurement suggests weak prolate deformation for the positive (A) and negative parity (C) dipole bands for In contrary to the triaxial deformation as predicted in the RMF calculation me06 (). Further measurement of the crossover E2 transitions in band A would establish this band as an ideal example of MR band owing to its small deformation of 0.08.

Vi Acknowledgments

Authors would like to thank the IUAC pelletron staff for providing good quality beam. The help and cooperation of the members of the INGA collaboration for setting up the array is acknowledged. This work was partially funded by the Department of Science and Technology, Government of India (No. IR/S2/PF-03/2003-I)


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