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A mean field calculation is carried out to obtain the equation of state (EoS) of nuclear matter from a density-dependent M3Y interaction (DDM3Y). The energy per nucleon is minimized to obtain ground state of the symmetric nuclear matter (SNM). The constants of density dependence of the effective interaction are obtained by reproducing the saturation energy per nucleon and the saturation density of SNM. The energy variation of the exchange potential is treated properly in the negative energy domain of nuclear matter. The EoS of SNM, thus obtained, is not only free from the superluminosity problem but also provides excellent estimate of nuclear incompressibility. The EoS of asymmetric nuclear matter is calculated by adding to the isoscalar part, the isovector component of M3Y interaction. The SNM and pure neutron matter EoS are used to calculate the nuclear symmetry energy which is found to be consistent with that extracted from the isospin diffusion in heavy-ion collisions at intermediate energies. The β equilibrium proton fraction calculated from the symmetry energy and related theoretical findings are consistent with the constraints derived from the observations on compact stars.

Half lives of the decays of spherical nuclei away from proton drip line by proton emissions are estimated theoretically. The quantum mechanical tunneling probability is calculated within the WKB approximation. Microscopic proton-nucleus interaction potentials are obtained by single folding the densities of the daughter nuclei with M3Y effective interaction supplemented by a zero-range pseudo-potential for exchange along with the density dependence. Parameters of the density dependence are obtained from the nuclear matter calculations. Spherical charge distributions are used for Coulomb interaction potentials. These calculations provide reasonable estimates for the observed proton radioactivity lifetimes of proton rich nuclei for proton emissions from 26 ground and isomeric states of spherical proton emitters.

Kanungo et al. ReplyThe Letter by Kanungo et al. [1] begins by highlighting the most important problem concerning the 23 O nucleus, i.e., the interaction cross section ( I ) cannot be explained using a usual shell model structure for 23 O but can only be understood under extreme assumptions of a very long density tail.It also shows that the one neutron removal momentum distribution (P jj ÿn ) can be understood with the usual shell model configuration of 23 O as well as other configurations. The most important fact is that both the (P jj ÿn ) and ( I ) cannot be consistently explained within any model.It must be clarified here that as stated in the Comment [2], the model used by us is not an inert core-plus-neutron model because the core excited state is considered.It should be further clarified that the reaction theory used for the calculation of single-particle removal cross sections ( sp ) in the Comment [3,4] is the same as that employed by us and is described in Ref. [5].Reference [3] (and [4] therein) clearly shows the use of the core-plus-neutron model and has Eqs. (2) and (3) which are identical to those of Ref.[5], Table I. The Comment then takes a sum of these sp weighted by spectroscopic factors (C 2 S) calculated in a many body shell model.One difference between our calculation and that of the Comment is that the Comment includes the ground state and all possible calculated bound excited states. We on the other hand consider only the first excited state of 22 O and the ground state.The other difference is that since the Comment employs the many body shell model for the calculation of spectroscopic factors such factors are greater than unity. In contrast, we discuss s and d wave strengths that add up to unity since the reaction model used is a core-plusneutron one.A spectroscopic factor greater than unity can arise in reality and also in the many body shell model when we discuss the knockout of neutrons from nuclei with more than one neutron in the valence orbit. However, the present reaction model treats this system as a core one neutron. The correct model to explain such a system is that of core multineutron which, as we pointed out, is lacking. The Comment claims to have a well-developed reaction model, but does not show it being a core multineutron one. If they wish to use spectroscopic factors from the shell model then, to be consistent, it is better to use sp calculated from a core multineutron model which should be different from the present ones.The Comment does not discuss at all the interaction cross section with their model. To establish the success of their model, they should be able to reproduce all observables of 23 O. Incidentally Fig. 29 in a recent review by Brown [6] shows that the interaction cross section for 23 O is not reproduced in the shell model employed. So the essential problem concerning this nucleus addressed in the Letter is not solved in their model.

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Theoretical estimates for the lifetimes of several isotopes of heavy elements with Z = 102-120 are presented by calculating the quantum mechanical tunneling probability in a WKB framework and using microscopic nucleus-nucleus potential obtained by folding the densities of interacting nuclei with the DDM3Y effective nuclear interaction. The α-decay half lives calculated in this formalism using the experimental Q-values are in good agreement over a wide range of experimental data. Half lives are also calculated using Q-values extracted from two mass formulae. The Viola-Seaborg-Sobiczewski (VSS) estimates of α-decay half lives with the same Q-values are presented for comparison. The half life calculations are found to be quite sensitive to the choice of Q-values. Comparison with the experimental data delineates the inadequacies of older mass predictions in the domain of heavy and superheavy elements as compared to the newer one by Muntian-Hofmann-Patyk-Sobiczewski, and highlights necessity of a more accurate mass formula which can predict Q-values with even higher precision.

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