... India 3 Department of Physics, University of Connecticut, Storrs, Connecticut 06269-3046, USA... more ... India 3 Department of Physics, University of Connecticut, Storrs, Connecticut 06269-3046, USA (Received 29 May 2009; published 10 September 2009) We ... We also perform calculations with central interactions (Minnesota [15] and Malfliet-Tjon V [16]) for 3 H, 4 He, and 6 Li as ...
We present a density functional theory which connects nuclear matter equation of state, which inc... more We present a density functional theory which connects nuclear matter equation of state, which incorporates clustering at low densities, with clustering in medium and heavy nuclei at the nuclear surface. This explains the large values of symmetry energy reported by Natowitz et al for densities < 0.01 fm-3 , in addition to the binding energies and charge rms radii of 367 spherical nuclei. The present theory which is partly macroscopic competes with other high quality microscopic-macroscopic approaches. Merits of the results with clustering and noclustering are discussed. We also make connection with realistic interactions (AV18+UIX/IL2) which have been used in ab initio calculations in sand p-shell nuclei and neutron matter. Theory predicts new situations and regimes to be explored both theoretically and experimentally. It is demonstrated that, due to clustering, the neutron skin thickness reduces significantly.
We present a phenomenological theory of nuclei that incorporates clustering at the nuclear surfac... more We present a phenomenological theory of nuclei that incorporates clustering at the nuclear surface in a general form. The theory explains the recently extracted large symmetry energy by Natowitz et al. at low densities of nuclear matter and is fully consistent with the static properties of nuclei. In phenomenological way clusters of all
Differential cross sections for ..cap alpha.. â´He elastic scattering have been calculated at in... more Differential cross sections for ..cap alpha.. â´He elastic scattering have been calculated at incident ..cap alpha..-particle momenta of 4.32, 5.07, and 7.0 GeV/c within the framework of Glauber multiple scattering theory. The full Glauber amplitude has been calculated using the Monte Carlo method for evaluating multidimensional integrals. We found that, in general, the more realistic double-Gaussian model for the density brings theory closer to experiment as compared to the generally used single-Gaussian model in some momentum transfer regions. Our results with the double-Gaussian model and an acceptable set of NN parameters are in fairly good agreement with the experimental data at 4.32 and 5.07 GeV/c.
We have calculated the kinetic energies of liquid and solid neon in the temperature range 9.235 ... more We have calculated the kinetic energies of liquid and solid neon in the temperature range 9.235 K. We have used the Wigner-Kirkwood expansion technique for the calculation of quantum corrections to the kinetic energy up to the order of ħ 6 in the expansion. All the averages ...
An improved variational ansatz is proposed and implemented for variational many-body wave functio... more An improved variational ansatz is proposed and implemented for variational many-body wave functions for light nuclei with nucleons interacting through Argonne (AV 18) and Urbana IX (UIX) three-nucleon interactions. The new ansatz is based upon variationally distinguishing between the various components of the two-body Jastrow and operatorial correlations, which are operated upon by three-body and spin-orbit correlations. We obtain noticeable improvement in the quality of the wave function and lowering of the energies compared to earlier results. The new energies are −8.38(1), −28.07(1), and −29.90(1) MeV for 3 H, 4 He, and 6 Li, respectively. Though, the present improved ansatz still fails to stabilize the 6 Li nucleus against a breakup into an α particle and a deuteron by 390 KeV; nonetheless, it is an improvement over previous studies.
In part 1 the effect of nuclear core dynamics cm the binding energies of Λ hy pernuclei is discu... more In part 1 the effect of nuclear core dynamics cm the binding energies of Λ hy pernuclei is discussed in the framework of variational correlated wave functions. In particular, we discuss a new rearrangement energy contribution and its effect on the core polarization. In part 2 we consider the interpretation of the Λ single-particle energy in terms of basic Λ-nuclear interactions using a local density approximation based on a fermi hypernetted chain calculation of the Λ binding to nuclear matter. To account for the data strongly repulsive 3-body AN Ν forces are required. Also in this framework we discuss core polarization for medium and heavier hypernuclei.
A simple method to sum elementary diagrams in the calculation of two-body and three-body distribu... more A simple method to sum elementary diagrams in the calculation of two-body and three-body distribution functions by the hypernetted-chain method is proposed. The method is based on the observation that the sum of the elementary diagrams has approximately the same spacial behavior as that of the lowest-order four-body elementary diagram. Thus the sums of two-point and three-point elementary diagrams may be approximated by a scaling constant times the lowest-order contribution. The scaling factor is determined by equating energies calculated with the Jackson-Feenberg and Pandharipande-Bethe expressions. Results of calculations of the energies and distribution functions of liquid~H e with the use of this method are reported, The results obtained with the McMillan correlation function are in almost exact agreement with the Monte Carlo results. Calculations with optimized correlation function having r tails are also reported.
We develop a Thomas Fermi theory to study the core polarization effects in Λ hypernuclei. Nuclei ... more We develop a Thomas Fermi theory to study the core polarization effects in Λ hypernuclei. Nuclei in the range of 10B to 243Am are included. Core polarization energies and changes in rms radii due to presence of Λ are calculated. It is shown that core polarization effects depend crucially on the effective compression modulus of the nucleus rather than on the compression modulus of the corresponding infinite nuclear matter.
An analysis of p-shell hypernuclei has been carried out within the shell model framework with cen... more An analysis of p-shell hypernuclei has been carried out within the shell model framework with central, charged-independent, state-dependent and weakly spin-dependent ..lambda..N forces of Skyrme type. The calculations reported here are preliminary.
Variational calculations for 6LambdaLambdaHe, 9LambdaBe and 10LambdaLambdaBe have been made with ... more Variational calculations for 6LambdaLambdaHe, 9LambdaBe and 10LambdaLambdaBe have been made with nalphaalpha-nLambdaLambda cluster models. Various alphaLambda potentials are considered, all of which reproduce BLambda(5LambdaHe). Some of the ValphaLambda are obtained from an alphaLambda model by a folding procedure using effective LambdaN and LambdaNN forces; realistic ValphaLambda are also obtained from 4N-Lambda Monte Carlo variational calculations of 5LambdaHe. These MC ValphaLambda include many-body effects which give a central hump even with only Lambda N forces. 9LambdaBe is overbound by about one MeV with realistic alphaalpha and alphaLambda potentials, even with reasonable estimates of LambdaN exchange effects which give a reduction ≅0.5 MeV. Repulsive LambdaNN forces which can account for the overbinding of 5LambdaHe give rise to a repulsive alphaalphaLambda potential which brings the calculated BLambda(9LambdaBe) into good agreement with the experimental energy. The LambdaL...
Variational Monte Carlo calculations of ground state separation energies B/\ of s-shell hypernucl... more Variational Monte Carlo calculations of ground state separation energies B/\ of s-shell hypernuclei and also of /\Be9 have been made for an Urbana type central space-exchange /\N potential consistent with /\p scattering and also including /\NN three-body forces. The s-shell hypernuclei are treated as A-body systems (A=baryon numbers) and /\Be9 is analysed as partially nine-body problem in the /\-2alpha model. The reduction of B/\ due to space-exchange /\N potential has been calculated for the s-shell hypernuclei for a range of interactions; both /\N+/\NN forces. For A=3,4,5 the exchange energy is approximately 0.04, 0.15, 0.5 MeV, respectively. For /\Be9 a much more limited study gives 1.3 MeV. These values are much larger than that for "soft " /\N+/\NN potentials when the correlation are weak.
Proceedings of the Conference on Advances in Radioactive Isotope Science (ARIS2014), 2015
We investigate the properties of asymmetric nuclear matter (ANM) which is consistent with cluster... more We investigate the properties of asymmetric nuclear matter (ANM) which is consistent with clustering at low densities of nuclear matter. Due to clustering, the equation of state of asymmetric nuclear matter demonstrates peculiar properties. It is shown that the ground of ANM has two separate phases of normal nuclear matter and neutron matter for Z N . This situation is at variance with the conventional picture of uniform distribution of neutrons and protons for ANM. Thus, this leads to an excellent understanding of the symmetry energy data of Wada et al. [1] in the density range of-3 fm 0.032-0.048. It is shown that inclusion of clustering at the nuclear surface is essential to explain about nuclei near the neutron drip line. The research incorporates 2149 nuclei [2] with 8 Z N, .
ABSTRACT We report results of variational calculations of liquid 4He with wave functions containi... more ABSTRACT We report results of variational calculations of liquid 4He with wave functions containing optimized two-body and three-body correlations. The hypernetted-chain (HNC) summation method is used, and the elementary and Abe diagrams are calculated with the scaling approximation. Comparisons with the existing Monte Carlo calculations suggest that this HNC-scaling method is almost exact. The logarithm of the three-body correlation of fijk contains terms having Pl(r̂ij·r̂ik), l=0, 1, and 2. As expected on theoretical grounds, the l=1 term of lnfijk dominates, while the l=0 and 2 terms give rather small changes in the binding energy. The fijk makes up ∼85% of the difference between the Jastrow and presumably exact Green&#39;s-function Monte Carlo (GFMC) energies. The best variational energies obtained with the HFDHE2 potential of Aziz et al. are within (2 ± 1)% of the GFMC and experimental results. The liquid structure function S(k) is also well explained by the variational wave function.
... g„(rJ ) . (2.2) The g„~(rjJ) give contributions to g, and xy =dd, de, and ee denote terms in ... more ... g„(rJ ) . (2.2) The g„~(rjJ) give contributions to g, and xy =dd, de, and ee denote terms in which neither i nor jis exchanged, jis exchanged, and both i and j are exchanged, respectively, The g~y are given by gdd(~;, ) fi(r;, )exp[Ndd(»;, )Edd(~;, ) 2.3a) ...
Summary The momentum distributionn(k) and the one-body density matrix ρ1(r,r&amp;amp;amp;amp... more Summary The momentum distributionn(k) and the one-body density matrix ρ1(r,r&amp;amp;amp;amp;#39; have been calculated in normal liquid3He atT=0. A variational wave function containing two-, three-body and backflow correlations has been used. The Fermi hypernetted chain technique has been employed and the elementary diagrams have been evaluated by the scaling approximation. The present estimate ofn(k) is in good agreement with the Monte Carlo
... India 3 Department of Physics, University of Connecticut, Storrs, Connecticut 06269-3046, USA... more ... India 3 Department of Physics, University of Connecticut, Storrs, Connecticut 06269-3046, USA (Received 29 May 2009; published 10 September 2009) We ... We also perform calculations with central interactions (Minnesota [15] and Malfliet-Tjon V [16]) for 3 H, 4 He, and 6 Li as ...
We present a density functional theory which connects nuclear matter equation of state, which inc... more We present a density functional theory which connects nuclear matter equation of state, which incorporates clustering at low densities, with clustering in medium and heavy nuclei at the nuclear surface. This explains the large values of symmetry energy reported by Natowitz et al for densities < 0.01 fm-3 , in addition to the binding energies and charge rms radii of 367 spherical nuclei. The present theory which is partly macroscopic competes with other high quality microscopic-macroscopic approaches. Merits of the results with clustering and noclustering are discussed. We also make connection with realistic interactions (AV18+UIX/IL2) which have been used in ab initio calculations in sand p-shell nuclei and neutron matter. Theory predicts new situations and regimes to be explored both theoretically and experimentally. It is demonstrated that, due to clustering, the neutron skin thickness reduces significantly.
We present a phenomenological theory of nuclei that incorporates clustering at the nuclear surfac... more We present a phenomenological theory of nuclei that incorporates clustering at the nuclear surface in a general form. The theory explains the recently extracted large symmetry energy by Natowitz et al. at low densities of nuclear matter and is fully consistent with the static properties of nuclei. In phenomenological way clusters of all
Differential cross sections for ..cap alpha.. â´He elastic scattering have been calculated at in... more Differential cross sections for ..cap alpha.. â´He elastic scattering have been calculated at incident ..cap alpha..-particle momenta of 4.32, 5.07, and 7.0 GeV/c within the framework of Glauber multiple scattering theory. The full Glauber amplitude has been calculated using the Monte Carlo method for evaluating multidimensional integrals. We found that, in general, the more realistic double-Gaussian model for the density brings theory closer to experiment as compared to the generally used single-Gaussian model in some momentum transfer regions. Our results with the double-Gaussian model and an acceptable set of NN parameters are in fairly good agreement with the experimental data at 4.32 and 5.07 GeV/c.
We have calculated the kinetic energies of liquid and solid neon in the temperature range 9.235 ... more We have calculated the kinetic energies of liquid and solid neon in the temperature range 9.235 K. We have used the Wigner-Kirkwood expansion technique for the calculation of quantum corrections to the kinetic energy up to the order of ħ 6 in the expansion. All the averages ...
An improved variational ansatz is proposed and implemented for variational many-body wave functio... more An improved variational ansatz is proposed and implemented for variational many-body wave functions for light nuclei with nucleons interacting through Argonne (AV 18) and Urbana IX (UIX) three-nucleon interactions. The new ansatz is based upon variationally distinguishing between the various components of the two-body Jastrow and operatorial correlations, which are operated upon by three-body and spin-orbit correlations. We obtain noticeable improvement in the quality of the wave function and lowering of the energies compared to earlier results. The new energies are −8.38(1), −28.07(1), and −29.90(1) MeV for 3 H, 4 He, and 6 Li, respectively. Though, the present improved ansatz still fails to stabilize the 6 Li nucleus against a breakup into an α particle and a deuteron by 390 KeV; nonetheless, it is an improvement over previous studies.
In part 1 the effect of nuclear core dynamics cm the binding energies of Λ hy pernuclei is discu... more In part 1 the effect of nuclear core dynamics cm the binding energies of Λ hy pernuclei is discussed in the framework of variational correlated wave functions. In particular, we discuss a new rearrangement energy contribution and its effect on the core polarization. In part 2 we consider the interpretation of the Λ single-particle energy in terms of basic Λ-nuclear interactions using a local density approximation based on a fermi hypernetted chain calculation of the Λ binding to nuclear matter. To account for the data strongly repulsive 3-body AN Ν forces are required. Also in this framework we discuss core polarization for medium and heavier hypernuclei.
A simple method to sum elementary diagrams in the calculation of two-body and three-body distribu... more A simple method to sum elementary diagrams in the calculation of two-body and three-body distribution functions by the hypernetted-chain method is proposed. The method is based on the observation that the sum of the elementary diagrams has approximately the same spacial behavior as that of the lowest-order four-body elementary diagram. Thus the sums of two-point and three-point elementary diagrams may be approximated by a scaling constant times the lowest-order contribution. The scaling factor is determined by equating energies calculated with the Jackson-Feenberg and Pandharipande-Bethe expressions. Results of calculations of the energies and distribution functions of liquid~H e with the use of this method are reported, The results obtained with the McMillan correlation function are in almost exact agreement with the Monte Carlo results. Calculations with optimized correlation function having r tails are also reported.
We develop a Thomas Fermi theory to study the core polarization effects in Λ hypernuclei. Nuclei ... more We develop a Thomas Fermi theory to study the core polarization effects in Λ hypernuclei. Nuclei in the range of 10B to 243Am are included. Core polarization energies and changes in rms radii due to presence of Λ are calculated. It is shown that core polarization effects depend crucially on the effective compression modulus of the nucleus rather than on the compression modulus of the corresponding infinite nuclear matter.
An analysis of p-shell hypernuclei has been carried out within the shell model framework with cen... more An analysis of p-shell hypernuclei has been carried out within the shell model framework with central, charged-independent, state-dependent and weakly spin-dependent ..lambda..N forces of Skyrme type. The calculations reported here are preliminary.
Variational calculations for 6LambdaLambdaHe, 9LambdaBe and 10LambdaLambdaBe have been made with ... more Variational calculations for 6LambdaLambdaHe, 9LambdaBe and 10LambdaLambdaBe have been made with nalphaalpha-nLambdaLambda cluster models. Various alphaLambda potentials are considered, all of which reproduce BLambda(5LambdaHe). Some of the ValphaLambda are obtained from an alphaLambda model by a folding procedure using effective LambdaN and LambdaNN forces; realistic ValphaLambda are also obtained from 4N-Lambda Monte Carlo variational calculations of 5LambdaHe. These MC ValphaLambda include many-body effects which give a central hump even with only Lambda N forces. 9LambdaBe is overbound by about one MeV with realistic alphaalpha and alphaLambda potentials, even with reasonable estimates of LambdaN exchange effects which give a reduction ≅0.5 MeV. Repulsive LambdaNN forces which can account for the overbinding of 5LambdaHe give rise to a repulsive alphaalphaLambda potential which brings the calculated BLambda(9LambdaBe) into good agreement with the experimental energy. The LambdaL...
Variational Monte Carlo calculations of ground state separation energies B/\ of s-shell hypernucl... more Variational Monte Carlo calculations of ground state separation energies B/\ of s-shell hypernuclei and also of /\Be9 have been made for an Urbana type central space-exchange /\N potential consistent with /\p scattering and also including /\NN three-body forces. The s-shell hypernuclei are treated as A-body systems (A=baryon numbers) and /\Be9 is analysed as partially nine-body problem in the /\-2alpha model. The reduction of B/\ due to space-exchange /\N potential has been calculated for the s-shell hypernuclei for a range of interactions; both /\N+/\NN forces. For A=3,4,5 the exchange energy is approximately 0.04, 0.15, 0.5 MeV, respectively. For /\Be9 a much more limited study gives 1.3 MeV. These values are much larger than that for "soft " /\N+/\NN potentials when the correlation are weak.
Proceedings of the Conference on Advances in Radioactive Isotope Science (ARIS2014), 2015
We investigate the properties of asymmetric nuclear matter (ANM) which is consistent with cluster... more We investigate the properties of asymmetric nuclear matter (ANM) which is consistent with clustering at low densities of nuclear matter. Due to clustering, the equation of state of asymmetric nuclear matter demonstrates peculiar properties. It is shown that the ground of ANM has two separate phases of normal nuclear matter and neutron matter for Z N . This situation is at variance with the conventional picture of uniform distribution of neutrons and protons for ANM. Thus, this leads to an excellent understanding of the symmetry energy data of Wada et al. [1] in the density range of-3 fm 0.032-0.048. It is shown that inclusion of clustering at the nuclear surface is essential to explain about nuclei near the neutron drip line. The research incorporates 2149 nuclei [2] with 8 Z N, .
ABSTRACT We report results of variational calculations of liquid 4He with wave functions containi... more ABSTRACT We report results of variational calculations of liquid 4He with wave functions containing optimized two-body and three-body correlations. The hypernetted-chain (HNC) summation method is used, and the elementary and Abe diagrams are calculated with the scaling approximation. Comparisons with the existing Monte Carlo calculations suggest that this HNC-scaling method is almost exact. The logarithm of the three-body correlation of fijk contains terms having Pl(r̂ij·r̂ik), l=0, 1, and 2. As expected on theoretical grounds, the l=1 term of lnfijk dominates, while the l=0 and 2 terms give rather small changes in the binding energy. The fijk makes up ∼85% of the difference between the Jastrow and presumably exact Green&#39;s-function Monte Carlo (GFMC) energies. The best variational energies obtained with the HFDHE2 potential of Aziz et al. are within (2 ± 1)% of the GFMC and experimental results. The liquid structure function S(k) is also well explained by the variational wave function.
... g„(rJ ) . (2.2) The g„~(rjJ) give contributions to g, and xy =dd, de, and ee denote terms in ... more ... g„(rJ ) . (2.2) The g„~(rjJ) give contributions to g, and xy =dd, de, and ee denote terms in which neither i nor jis exchanged, jis exchanged, and both i and j are exchanged, respectively, The g~y are given by gdd(~;, ) fi(r;, )exp[Ndd(»;, )Edd(~;, ) 2.3a) ...
Summary The momentum distributionn(k) and the one-body density matrix ρ1(r,r&amp;amp;amp;amp... more Summary The momentum distributionn(k) and the one-body density matrix ρ1(r,r&amp;amp;amp;amp;#39; have been calculated in normal liquid3He atT=0. A variational wave function containing two-, three-body and backflow correlations has been used. The Fermi hypernetted chain technique has been employed and the elementary diagrams have been evaluated by the scaling approximation. The present estimate ofn(k) is in good agreement with the Monte Carlo
Uploads
Papers by Qamar Usmani