arXiv subjects
Publications and source records attributed to A. Arima.
In this talk we shall show our recent results in understanding the spin$^{\rm parity}$ 0$^+$ ground state (0 g.s.) dominance of many-body systems. We propose a simple approach to predict the spin $I$ g.s. probabilities which does not require the diagonalization of a Hamiltonian with random interactions. Some findings related to the 0 g.s. dominance will also be discussed.
In this talk I shall discuss some regularities of many-body systems in the presence of random interactions and regularities of a single-$j$ shell for the $J$ pairing interaction which works only when two particles are coupled to spin $J$. I shall first explain an empirical rule to predict the spin $I$ ground state probability. Then I shall present some interesting results of a single-$j$ shell under the $J$ pairing interaction. Last I shall discuss some preliminary results of binding energies in the presence of random two-body interactions.
The connection between the enhancement factor (1+kappa) of the photonuclear E1 sum rule and the orbital angular momentum g-factor (gl) of a bound nucleon is investigated in the framework of the Landau-Migdal theory for isospin asymmetric nuclear matter. Special emphasis is put on the role of gauge invariance to establish the kappa-gl relation. By identifying the physical processes which are taken into account in kappa and gl, the validity and limitations of this relation are discussed. The connections to the collective excitations and to nuclear Compton scattering are also shown.
We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = Jmax pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular for those with total angular momenta I le 2j. For I=0 eigenstates of four fermions in a single-j shell we show that there is only one non-zero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems.
In this paper we report our systematic calculations of angular momentum $I$ ground state probabilities ($P(I)$) of boson systems with spin $l$ in the presence of random two-body interactions. It is found that the P(0) dominance is usually not true for a system with an odd number of bosons, while it is valid for an even number of bosons, which indicates that the P(0) dominance is partly connected to the even number of identical particles. It is also noticed that the $P(I_{max})$'s of bosons with spin $l$ do not follow the 1/N ($N=l+1$, referring to the number of independent two-body matrix elements) relation. The properties of the $P(I)$'s obtained in boson systems with spin $l$ are discussed.
In this paper we present the systematics of excitation energies for even-even nuclei in two regions: the 50$<$Z$\le$66, 82$<$N$\le$104 region, and the 66$<$Z$<$82, 82$<$N$\le$104 region. Using the $N_pN_n$ scheme, we obtain compact trajectories for the ground band as well as quasi-$β$ and quasi-$γ$ bands. This suggests that the $N_pN_n$ scheme is useful even if one extends it to non-yrast levels, and thus can serve as a general tool to disclose new types of structural evolution for higher excitations, besides the yrast states which have been investigated extensively. It is highlighted that deformations in non-yrast quasibands of nuclei with $Z \sim 80$ and $N \sim 104$ are often very different from those in the ground bands.
We present in this paper empirical formulas for the number of angular momentum I states for three and four identical fermions or bosons. In the cases with large I we prove that the number of states with the same ${\cal M}$ and n but different J is identical if $I \ge (n-2)J - {1/2} (n-1)(n-2)$ for fermions and $I \ge (n-2)J$ for bosons, and that the number of states is also identical for the same ${\cal M}$ but different n and J if ${\cal M} \le $min(n, 2J+1 - n) for fermions and for ${\cal M} \le $min(n, 2J) for bosons. Here ${\cal M} =I_{max}-I$, n is the particle number, and J refers to the angular momentum of a single-particle orbit for fermions, or the spin L carried by bosons.
To be replaced with a revised version.
Low-lying collective states involving many nucleons interacting by a random ensemble of two-body interactions (TBRE) are investigated in a collective SD-pair subspace, with the collective pairs defined dynamically from the two-nucleon system. It is found that in this truncated pair subspace collective vibrations arise naturally for a general TBRE hamiltonian whereas collective rotations do not. A hamiltonian restricted to include only a few randomly generated separable terms is able to produce collective rotational behavior, as long as it includes a reasonably strong quadrupole-quadrupole component. Similar results arise in the full shell model space. These results suggest that the structure of the hamiltonian is key to producing generic collective rotation.
In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)'s, angular momenta I ground state (g.s.) probabilities, of a few solvable cases, such as fermions in a small single-j shell and d boson systems, is given. This method is generalized to predict P(I)'s of more complicated cases, such as even or odd number of fermions in a large single-j shell or a many-j shell, d-boson, sd-boson or sdg-boson systems, etc. By this method we are able to tell which interactions are essential to produce a sizable P(I) in a many-body system. The g.s. probability of maximum angular momentum $I_{max}$ is discussed. An argument on the microscopic foundation of our approach, and certain matrix elements which are useful to understand the observed regularities, are also given or addressed in detail. The low seniority chain of 0 g.s. by using the same set of two-body interactions is confirmed but it is noted that contribution to the total 0 g.s. probability beyond this chain may be more important for even fermions in a single-j shell. Preliminary results by taking a displaced two-body random ensemble are presented for the I g.s. probabilities.
In this paper, we discuss the regularities of energy of each angular momentum $I$ averaged over all the states for a fixed angular momentum (denoted as $\bar{E}_I$'s) in many-body systems interacting via a two-body random ensemble. It is found that $\bar{E}_I$'s with $I \sim I_{min}$ (minimum of $I$) or $I_{max}$ have large probabilities (denoted as ${\cal P}(I)$) to be the lowest, and that ${\cal P}(I)$ is close to zero elsewhere. A simple argument based on the randomness of the two-particle cfp's is given. A compact trajectory of the energy $\bar{E}_I$ vs. $I(I+1)$ is found to be robust. Regular fluctuations of the $P(I)$ (the probability of finding $I$ to be the ground state) and ${\cal P}(I)$ of even fermions in a single-$j$ shell and boson systems are found to be reverse, and argued by the dimension fluctuation of the model space. Other regularities, such as why there are 2 or 3 sizable ${\cal P}(I)$'s with $I\sim I_{min}$ and ${\cal P}(I) \ll {\cal P}(I_{max})$'s with $I\sim I_{max}$, why the coefficients $C$ defined by $<\bar{E}_I >$=$CI(I+1)$ is sensitive to the orbits and not sensitive to particle number, are found and studied for the first time.
We point out that the time reversal invariance, which was further interpreted by Velazquez et al. using the behaviors of $E_{cI}$ and $σ_I^2$, can not be the origin of the 0 g.s. dominance, as was pointed out previously by Bijker et al, and that the discussion by Velazquez et al. using a displaced TBRE is not true in general.
We propose a simple approach to predict the angular momentum I ground state (I g.s.) probabilities of many-body systems that does not require the diagonalization of hamiltonians with random interactions. This method is found to be applicable to {\bf all} cases that have been discussed: even and odd fermion systems (both in single-j and many-j shells), and boson (both sd and sdg) systems. A simple relation for the highest angular momentum g.s. probability is found. Furthermore, it is suggested for the first time that the 0g.s. dominance in boson systems and in even-fermion systems is given by two-body interactions with specific features.
For single-$j$ shells with $j={7/2}, {9/2}$ and 11/2, we relate the large probability of $I^+$ ground states to the largest (smallest) coefficients $α^J_{I(v β)} = $, where $n$ is the particle number, $v$ is the seniority, $β$ is an additional quantum number, and $I$ is the angular momentum of the state. Interesting regularities of the probabilities of $I^+$ ground states are noticed and discussed for 4-particle systems. Several counter examples of the $0^+$ ground state (0GS) predominance are noticed for the first time.
Based on the Relativistic continuum Hartree-Bogoliubov (RCHB) theory, the pseudo-spin approximation in exotic nuclei is investigated in Zr and Sn isotopes from the proton drip line to the neutron drip line. The quality of the pseudo-spin approximation is shown to be connected with the competition between the centrifugal barrier (CB) and the pseudo-spin orbital potential (PSOP). The PSOP depends on the derivative of the difference between the scalar and vector potentials $dV/dr$. If $dV/dr = 0$, the pseudo-spin symmetry is exact. The pseudo-spin symmetry is found to be a good approximation for normal nuclei and to become much better for exotic nuclei with highly diffuse potential, which have $dV/dr \sim 0$. The energy splitting of the pseudo-spin partners is smaller for orbitals near the Fermi surface (even in the continuum) than the deeply bound orbitals. The lower components of the Dirac wave functions for the pseudo-spin partners are very similar and almost equal in magnitude.
In this paper, eit is shown for a single-$j$ shell that the intrinsic excitations induced by the quadrupole-quadrupole interaction can be viewed as that due to the inverted surface-delta interaction whose multipole-pairing component with the largest spin is the dominant term and is attractive. This allow us to trace the origin of the recently introduced optimum pair description of rotation and leads naturally to analytical expressions for the rotational energies for the various bands in a single $j$-shell with the quadrupole-quadrupole interaction.