Session KF: Theory: Coulomb/Structure/Statistical/Beta-decay

Coulomb distorted nuclear matrix elements in momentum space: I. Formal aspects

(d,p) reactions are an important tool to reveal nuclear structure. In order to treat elastic scattering, transfer and breakup reactions on the same footing,it is advantageous to view the a (d,p) reaction as three-body problem p+n+A within a Faddeev framework. A screening and renormalization technique for including the Coulomb interaction has been used in pioneering a Faddeev approach in (d,p) reactions for light nuclei [1]. It turns out that this procedure is not suited for reaction with heavy nuclei, since it becomes numerically unstable [2]. Therefore a new approach has been suggested by Mukhamedzhanov [3] by formulating the Faddeev equations in a Coulomb basis instead of plane wave basis. In order to test the feasibility of this approach we calculate as first step Coulomb distorted nuclear matrix elements for a variety of nuclei (including 208Pb) for partial waves from l=0 to l=20. Insights and techniques for this will be presented. \\[4pt] [1] A. Deltuva, A. C. Fonseca, and P. U. Sauer, Phys. Rev. C71, 054005 (2005).\\[0pt] [2] F.M. Nunes and A. Deltuva, Phys. Rev. C84, 034607 (2011).\\[0pt] [3] A. M. Mukhamedzhanov et al., Phys. Rev. C86, 034001 (2012).   

Coulomb distorted nuclear matrix elements in momentum space. II. Computational aspects

$(d,p)$ reactions are an important tool to reveal nuclear structure. In order to treat elastic scattering, transfer and breakup reactions on the same footing, it is advantageous to view a $(d,p)$ reaction as three-body problem $p+n+A$ within a Faddeev framework. In order to test a new Faddeev based approach that exactly includes the Coulomb interaction [1] and is valid for light as well as heavy nuclei, as first step Coulomb distorted nuclear matrix elments are calculated. Numerical aspects are explicitly discussed, and results for a variety of nuclei (including $^{208}$Pb) will be presented using separable nuclear optical potentials as input.\\[4pt] [1] A.M. Mukhamedzhanov et al. Phys. Rev. C 86, 034001 (2012).   

Nuclear Matrix Elements for Tensor Interactions that Violate Local Lorentz Invariance

The principle of local Lorentz invariance can be tested by measurements using a $^{21}$Ne-Rb-K comagnetometer [M. Smiciklas, J. M. Brown, L. W. Cheuk, S. J. Smullin and M. V. Romalis, Phys. Rev. Lett. {\bf 107}, 171604 (2011)]. This experiment puts strong limits on the possible anisotropy in the maximum attainable velocity for a massive particle. In order to convert from magnetic field units one needs the nuclear matrix element of the quadrupole momentum tensor operator proportional to $2p_z^2-p_x^2-p_y^2$ for the $3/2^+$ ground state of $^{21}$Ne. In the paper above the simple $d_{3/2}$ single-particle model was used. We use the full sd-shell model wavefunctions. We also consider the effect of core polarization. Results for $^{131}$Xe and $^{201}$Hg are also considered.   

Almost Universal Behavior in Many-Body Hamiltonians

We think of different interactions having very different properties. Yet studies of many-body systems with random two-body interactions show qualitatively similar behavior. As part of dissecting this phenomenon, I present new results on nearly universal behaviors among widths of many-body Hamiltonians. This suggests many-body systems are even more tightly constrained by symmetry than previously understood.   

Effective interactions in $sd$-shell from \textit{ab-initio} shell model with a core

We perform \textit{ab-initio} no-core shell model calculations for $A=18$ and $19$ nuclei in a $4\hbar\Omega$ model space using JISP16 and CD-Bonn nucleon-nucleon potentials and project the many-body Hamiltonians onto the $0\hbar\Omega$ model space to construct the effective $A$-body Hamiltonians in the $sd$-shell. We separate the effective $A$-body Hamiltonians with $A=18$ and $A=19$ into inert core, one- and two-body pieces. Then, these core, one- and two-body pieces are used to perform a standard shell model calculations for the $A=18$ and $A=19$ systems. Finally, we compare the standard shell model results with the exact no-core shell model results for the $A=18$ and $A=19$ systems.   

Level densities of nickel isotopes: microscopic theory versus experiment

The shell model Monte Carlo (SMMC) approach has enabled the microscopic calculation of nuclear level densities in model spaces that are many orders of magnitude larger than what can be treated with conventional diagonalization methods. The density calculated in the SMMC method is the \emph{state} density, in which each level with spin $J$ is counted $2J+1$ times. However, the experimentally measured density is often the \emph{level} density, in which each level is counted just once irrespective of its $2J+1$ magnetic degeneracy. Recently our group introduced a spin projection method~[1] that enables the direct calculation of the level density in the SMMC approach. We present an application of this method to a family of nickel isotopes $^{59{\textrm -}64}$Ni in the complete $pfg_{9/2}$ shell~[2]. We find the calculated level densities to be in close agreement with level densities obtained from recent measurements of proton evaporation spectra~[3] and from level counting data. We also compare our results with neutron resonance data.\\[4pt] [1] Y. Alhassid, M. Bonett-Matiz, S. Liu, and H. Nakada, arXiv:1304.7258.\\[0pt] [2] M. Bonett-Matiz, A. Mukherjee, and Y. Alhassid, arXiv:1305.0250.\\[0pt] [3] A. V. Voinov {\it et al.}, EPJ Web of Conferences {\bf 21}, 05001 (2012).   

Law of Electron Emission Beta Decay

All atoms start as barren dark matter NeutroniumA string-like quark threesomes. The Nuclear Strong Force for string-like quark threesomes has its maximum when the ratio of the accumulated charge on the positive quarks to the accumulated charge on the negative quarks is 77\%. All NeutroniumAs, with atomic number zero have the smallest possible accumulated charge ratio 50\%. All nuclei having an accumulated charge ratio less than 77\% will beta decay by electron emission. All 233 least massive nuclei agree with this law. All nuclei with an accumulated charge ratio larger than 77\% are stable against electron emission beta decay. The most stable nucleus, the proton, has an accumulated charge ratio 200\%. Nature provides nuclei with an accumulated charge ratio larger than 77\% with a variety of acts they might use to emulate the proton. They can internally redistribute their charge, emit a positron or capture an electron.