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L. Zamick

Publications and source records attributed to L. Zamick.

At least 55 records · Page 3Linked to original sources
arXiv2000

Dependence of the Shell-Model Single-Particle Energies on Different Components of the Nucleon-Nucleon Interaction

The spin-orbit splittings in the spectra of nuclei with mass numbers 5, 15 and 17 are studied within the framework of shell-model configuration mixing calculations including 2$\hbar ω$ excitations. The contributions of the two-body spin-orbit and tensor components of the nucleon-nucleon interaction are studied in various model spaces. It is found that the effects of the two-body spin-orbit interaction are dominant and quite sensitive to the size of the model-space considered. The effects of the tensor interaction are weaker. The correlations effects which are included in the larger (0+2) $\hbar ω$ shell-model space reduce the spin-orbit splitting in the case of A=5 by 20%, and enhance it for A=15 by about the same 20%. However, it is found that the correlations have a very small effect on the $d_{3/2} - d_{5/2}$ splitting in A=17.

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arXiv1999

Vanishing Gamow-Teller Transition Rate for A=14 and the Nucleon-Nucleon Interaction in the Medium

The problem of the near vanishing of the Gamow-Teller transition ($GT$) in the A=14 system between the lowest $J=0^+~ T=1$ and $J=1^+~ T=0$ states is revisited. The model space is extended from the valence space $(p^{-2})$ to the valence space plus all 2$\hbar ω$ excitations. The question is addressed as to what features of the effective nucleon-nucleon interaction in the medium are required to obtain the vanishing $GT$ strength in this extended space. It turns out that a combination of a realistic strength of the tensor force combined with a spin-orbit interaction which is enhanced as compared to the free interaction yields a vanishing $GT$ strength. Such an interaction can be derived from a microscopic meson exchange potential if the enhancement of the small component of the Dirac spinors for the nucleons is taken into account.

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arXiv1999

Systematics of the Quadrupole-Quadrupole Interaction and Convergence Properties

Our main concern in this work is to show how higher shell admixtures affect the spectrum of a Q.Q interaction. We first review how, in the valence space, the familiar SU(3) result for the energy spectrum can be obtained using a coordinate space Q.Q interaction rather than the Elliott one which is symmetric in r and p. We then reemphasize that the Elliott spectrum goes as L(L+1) where L is the orbital angular momentum. While in many cases this is compatible with the rotational formula which involves I(I+1), where I is the total angular momentum, there are cases, e.g. odd-odd nuclei, where there is disagreement. Finally, we consider higher shell admixtures and devise a scheme so as to obtain results, with the Q.Q interaction, which converge as the model spaces are increased. We consider not only ground state rotational bands but also those that involve intruder states.

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arXiv1999

The Interference Term between the Spin and Orbital Contributions to M1 Transitions

We study the cross-correlation between the spin and orbital parts of magnetic dipole transitions M1 in both isoscalar and isovector channels. In particular, we closely examine certain cases where $\sum B(M1)$ is very close to $\sum B(M1)_σ + \sum B(M1)_l$, implying a cancellation of the summed interference terms. We gain some insight into this problem by considering special cases approaching the SU(3) limit, and by examining the behaviour of single-particle transitions at the beginning and towards the end of the s-d shell.

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arXiv1999

The Effects of Deformation on Isovector Electromagnetic and Weak Transition Strengths

The summed strength for transitions from the ground state of $^{12}C$ via the operators $\vec{s}t, \vec{\ell}t, rY't, r[Y's]^λt$ and $r[Y'\ell]^λt$ are calculated using the $ΔN = 0$ rotational model. If we choose the z component of the isospin operator $t_{z}$, the above operators are relevant to electromagnetic transitions; if we choose $t_{+}$ they are relevant to weak transitions such as neutrino capture. In going from the spherical limit to the asymptotic (oblate) limit the strength for the operator $\vec{s} t$ decreases steadily to zero; the strength for the operator $\vec{\ell}τ$ (scissors mode) increases by a factor of three. For the last three operators - isovector dipole, spin dipole and orbital dipole (including the twist mode) it is shown that the summed strength is independant of deformation. The main difference in the behavior is that for the first two operators we have in-shell transitions whereas for the last three operators the transitions are out of shell.

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arXiv1998

Anomalous Band Structure in Odd-Odd Nuclei with the Quadrupole-Quadrupole Interaction

We perform shell model calculations in odd-odd nuclei using a quadrupole-quadrupole interaction and single-particle splittings chosen so as to obtain the SU(3) results. Elliott had shown that such an interaction gives rotational bands for which the energies go as I(I+1). This is certainly true for eve-even and for odd-even or even-odd nuclei with $K\neq 1/2$. We have looked at odd-odd nuclei e.g $^{22}Na$ and found somewhat different behaviour. In $^{22}Na$ the $I=1^+_1 T=0$ and $I=0^+_1 T=1$ states are degenerate, and a rotational band built on the $I=0^+_1 T=1$ state behaves in a normal fashion. For the $I+1^+_1 T=0$ band however, we find that the energy is given by $E(I)-E(1^+_1)=AI(I+1)$. This differs from the `normal' behaviour which would be $E(I)-E(1^+_1)=AI(I+1)-2A$.

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arXiv1998

The Question of Low-Lying Intruder States in $^8Be$ and Neighboring Nuclei

The presence of not yet detected intruder states in $^{8}Be$ e.g. a $J=2^{+}$ intruder at 9 $MeV$ excitation would affect the shape of the $β^{\mp }$-delayed alpha spectra of $^{8}Li$ and $^{8}B$. In order to test the plausibility of this assumption, shell model calculations with up to $4\hbar ω$ excitations in $^{8}Be$ (and up to $2\hbar ω$ excitations in $^{10}Be$) were performed. With the above restrictions on the model spaces, the calculations did not yield any low-lying intruder state in $^{8}Be$. Another approach -the simple deformed oscillator model with self-consistent frequencies and volume conservation gives an intruder state in $^{8}Be$ which is lower in energy than the above shell model results, but its energy is still considerably higher than 9 $MeV$.

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arXiv1997

Canonical and Microcanonical Ensemble Approaches to Bose-Einstein Condensation: The Thermodynamics of Particles in Harmonic Traps

The thermodynamic properties of bosons moving in a harmonic trap in an arbitrary number of dimensions are investigated in the grand canonical, canonical and microcanonical ensembles by applying combinatorial techniques developed earlier in statistical nuclear fragmentation models. Thermodynamic functions such as the energy and specific heat are computed exactly in these ensembles. The occupation of the ground or condensed state is also obtained exactly, and signals clearly the phase transition. The application of these techniques to fermionic systems is also briefly discussed.

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arXiv1997

Are There Low-Lying Intruder States in ^8Be?

We allow up to $4 \hbarω$ excitations in $^8Be$ relative to the basic configuration $(0s)^4(0p)^4$ in order to see if there are low-lying intruder states in $^8Be$. We use three interactions $-χQ \cdot Q, -χQ \cdot Q$ + spin-orbit, and a realistic (x,y) interaction, where for $x=1,y=1$ one gets values for the spin-orbit and tensor interactions which correspond closely to those of a non-relativistic $G$ matrix such as Bonn A. For the three interactions considered, if we allow up to $2 \hbar ω$ excitations we get the energy of the lowest $J=0^+$ intruder state to be at 32.1 MeV, 30.1 MeV and 33.8 MeV, respectively. If we allow up to $4 \hbarω$ excitations the corresponding values are 26.5 MeV, 26.5 MeV and 28.7 MeV. We thus support the statement made by E. Warburton in his 1986 $R$ matrix analysis of the $β^{\mp}$-delayed alpha spectra from the decay of $^8Li$ and $^8B$ that ``satisfactory fits are obtained without introducing intruder states below 26-MeV excitations'' (Phys. Rev. C 33, 303(1986)). In $^{10}Be$ however, with the first two ``$Q \cdot Q$'' interactions, we get (with up to $2 \hbar ω$ excitations) low-lying intruder states at 9.7 MeV and 11.9 MeV respectively. Thus the presence of low-lying intruder states in $^{10}Be$ (the $0^+_2$ state at 6.179 MeV may or may not be an intruder) does not imply that there are low-lying intruder states in $^8Be$.

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arXiv1997

The effects of varying the strengths of tensor and spin-orbit interactions on M1 and E2 rates in ^{12}C: Comparison of results in $ΔN = 0$ and $ΔN = 0 + 2\hbarω$ spaces}

The energies and transition rates to $J=1^{+} T=1$ and $J=2^{+} T=0,1$ states in ^{12}C with matrix elements fitted to realistic $G$ matrix elements obtained in non-relativistic approaches are studied. Then the effects of varying the strengths of the two-body tensor and spin-orbit interactions are also considered. The calculations are done in both a small space (0p) and a large space (0p + $2\hbarω$). In the small space the B(M1) from ground to the $J=1^{+} T=1$ is enhanced and gets closer to experiment if the strength of the spin-orbit interaction is increased and/or if that of the tensor interaction is made weaker. In a large space the spin B(M1) gets reduced by almost a factor of two. A `self-weakening' mechanism for the tensor interaction which succeeded in explaining anomalies in other nuclei does not seem to work for this case.

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arXiv1997

Comparison of Fermion SU(3) and Boson SU(3) models for scissors mode excitations

For a $Q \cdot Q$ interaction the energy weighted sum rule for isovector orbital magnetic dipole transitions is proportional to the difference $\sum B(E2, isoscalar) - \sum B(E2, isovector)$, not just to $\sum B(E2, physical)$. This fact is important in ensuring that one gets the correct limit as one goes to nuclei, some of which are far from stability, for which one shell (neutron or proton) is closed. In $0p$ shell calculations for the even-even Be isotopes it is shown that the Fermion SU(3) model and Boson SU(3) model give different results for the energy weighted scissors mode strengths.

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arXiv1996

Topics Concerning the Quadrupole-Quadrupole Interaction

We address some properties of the quadrupole-quadrupole ($Q \cdot Q$) interaction in nuclear studies. We first consider how to restore $SU(3)$ symmetry even though we use only coordinate and not momentum terms. Using the Hamiltonian $H=\sum_i (p^2/2m + m/2 ω^2 r_i^2) -χ\sum_{i < j}Q(i) \cdot Q(j) - χ/2 \sum_i Q(i) \cdot Q(i)$ with $Q_μ=r^2 Y_{2,μ}$, we find that only 2/3 of the single-particle splitting ($ε_{0d}-ε_{1s}$) comes from the diagonal term of $Q \cdot Q$ -the remaining 1/3 comes from the interaction of the valence nucleus with the core. On another topic, a previously derived relation, using $Q \cdot Q$, between isovector orbital $B(M1)$ (scissors mode) and the ``difference'' ($B(E2, isoscalar)-B(E2, isovector)$) is discussed. It is shown that one needs the isovector $B(E2)$ in order that one get the correct limit as one goes to nuclei sufficiently far from stability so that one subshell (neutron or proton) is closed.

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arXiv1996

Quadrupole-quadrupole interaction calculations which include N=2 mixing

We carry out a study of the study of the $Q \cdot Q$ interaction in a model space which consists of several nucleons in an open shell and all $2 \hbar ω$ excitations. This interaction is $ -t (X_o/2) Q \cdot Q$, where for t=1 we get the `accepted strength'. In the $0p$ space, the spectrum would scale with $t$. In this space, the $2^+_1$ and $2^+_2$ states of $^{10}$Be are degenerate, as are the [330] and [411] sets of $J=0^+, 1^+$ and $2^+$ triplets. When $2 \hbar ω$ admixtures are included, the degeneracies are removed. For $t \geq 1.8$ we have new ground state and a new $2_1^+$ state. These are states in which two particles are excited from the $0p$ to the $1s-0d$ shell. There is no mixing of these 2p-2h states with the other states. For these 2p-2h states the occupancy for 0s,0p,1s-0d and 1p-of are 4,4,2 and 0 respectively.

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arXiv1996

Effects of the Spin-Orbit and Tensor Interactions on the $M1$ and $E2$ Excitations in Light Nuclei

The effects of varying the spin-orbit and tensor components of a realistic interaction on $M1$ excitation rates and $B(E2)'s$ are studied on nuclei in the $0p$ and $1s-0d$ shells. Not only the total $M1$ but also the spin and orbital parts separately are studied. The single-particle energies are first calculated with the same interaction that is used between the valence nucleons. Later this stringent condition is relaxed somewhat and the $1s$ level is raised relative to $0d$. For nuclei up to $^{28}Si$, much better results i.e stronger $B(M1)$ rates are obtained by increasing the strength of the spin-orbit interaction relative to the free value. This is probably also true for $^{32}S$, but $^{36}Ar$ presents some difficulties. The effects of weakening the tensor interaction are also studied. On a more subtle level, the optimum spin-orbit interaction in the lower half of the $s-d$ shell, as far as $M1$ excitations are concerned, is substantially larger than the difference $E(J=3/2^+)_1-E(J=5/2^+)_1=5.2~MeV$ in $^{17}O$. A larger spin-orbit splitting is also needed to destroy the triaxiality in $^{22}Ne$. Also studied are how much $M1$ orbital and spin strength lies in an observable region and how much is buried in the grass at higher energies. It is noted that for many nuclei the sum $B(M1)_{orbital}+B(M1)_{spin}$ is very close to $B(M1)_{total}$, indicating that the summed cross terms are very small.

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