arXiv subjects

L. Zamick

Publications and source records attributed to L. Zamick.

65 records · Page 4Linked to original sources

arXiv1996

Non-trivial aspects of the onset of nuclear collectivity: Static moments

We consider several topics concerning static magnetic dipole and electric quadrupole moments ($μ$ and $Q$) as signatures of the onset of nuclear collectivity. Having previously noted that in $^{50}\mbox{Cr}$ there is an abrupt change of sign in $Q$ of yrast states with $J^π=10^+, 12^+$, and $14^+$ relative to lower $J$ states, we discuss whether these states are oblate or prolate. We next show that configuration mixing leads to much larger changes in $Q$ than in $μ$. We then look for other bands of interest in $^{50}\mbox{Cr}$. Finally we discuss the Jolos-von Brentano relationship which relates $Q$ of $2^+_1$ states to $B({\rm E2})$'s for transitions from and to the $2^+_1$ states.

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arXiv1995

Change of shape in the yrast sequence in 50Cr

In shell model calculations for the yrast even spin states of 50Cr, the static quadrupole moments of the low spin states 2+_1 and 4+_1 are negative but those of the high spin states 10+_1, 12+_1 and 14+_1 are positive. Even spin states beyond the single j shell limit, J_max=14, again have negative moments. While the B(E2)'s for the J -> J-2 transitions are strongest along the yrast path for J <= 8, it is found that the transition from the second J=10 state to the first J=8 state (10+_2 -> 8+_1) is much stronger than the 10+_1 -> 8+_1 transition. We also note that while the 16+_1 -> 14+_1 transition is weak, the 16+_1 -> 14+_2 is quite strong.

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arXiv1995

The Isovector Quadrupole-Quadrupole Interaction Used in Shell Model Calculations

An interaction $-χQ\cdot Q(1+B\vecτ(1)\cdot \vecτ(2))$ is used in a shell model calculation for $^{10}Be$. Whereas for $B=0$ the $2_1^+$ state is two-fold degenerate, introducing a negative $B$ causes an `isovector' $2^+$ state to come down to zero energy at $B=-0.67$ and an $S=1~L=1$ triplet ($J=0^+,~1^+,~2^+$) to come down to zero energy at $B=-0.73$. These are undesirable properties, but a large negative $B$ is apparently needed to fit the energy of the isovector giant quadrupole resonance.

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arXiv1995

Scissors Modes and Spin Excitations in Light Nuclei including $ΔN$=2 excitations: Behaviour of $^8Be$ and $^{10}Be$

Shell model calculations are performed for magnetic dipole excitations in $^8{Be}$ and $^{10}{Be}$ in which all valence configurations plus $2\hbarω$ excitations are allowed (large space). We study both the orbital and spin excitations. The results are compared with the `valence space only' calculations (small space). The cumulative energy weighted sums are calculated and compared for the $J=0^+$ $T$=0 to $J=1^+$ $T$=1 excitations in $^8{Be}$ and for $J=0^+$ $T$=1 to both $J=1^+$ $T$=1 and $J$=$1^+$ $T$=2 excitations in $^{10}{Be}$. We find for the $J=0^+$ $T$=1 to $J=1^+$ $T$=1 isovector {\underline {spin}} transitions in $^{10}{Be}$ that the summed strength in the {\underline {large}} space is less than in the {\underline {small}} space. We find that the high energy energy-weighted isovector orbital strength is smaller than the low energy strength for transitions in which the isospin is changed, but for $J=0^+$ $T$=1 to $J=1^+$ $T$=1 in $^{10}{Be}$ the high energy strength is larger. We find that the low lying orbital strength in $^{10}{Be}$ is anomalously small, when an attempt is made to correlate it with the $B(E2)$ strength to the lowest $2^+$ states. On the other hand a sum rule of Zheng and Zamick which concerns the total $B(E2)$ strength is reasonably satisfied in both $^8{Be}$ and $^{10}{Be}$. The Wigner supermultiplet scheme is a useful guide in analyzing shell model results. In $^{10}Be$ and with a $Q \cdot Q$ interaction the T=1 and T=2 scissors modes are degenerate, with the latter carrying 5/3 of the T=1 strength.

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arXiv1994

A Limited Symmetry Found by Comparing Calculated Magnetic Dipole Spin and Orbital Strengths in $^4\mbox{He}$

Allowing for $2$$\hbar ω$ admixtures in $^4\mbox{He}$ we find that the summed magnetic dipole isovector orbital and spin strengths are equal. This indicates a symmetry which is associated with interchanging the labels of the spin with those of the orbit. Where higher admixtures are included, the orbital sum becomes larger than the spin sum, but the sums over the low energy region are still nearly the same.

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arXiv1994

Self weakening of the tensor interaction in a nucleus

We examine several ``landmarks'' for the effects of the tensor interaction on the properties of light nuclei. These were usually discussed in the context of small-space shell-model calculations. We show, using $G$ matrices derived from a realistic nucleon-nucleon potential, that when the model space is small (e.g., $0\hbarω$), these effects are overestimated, indicating that the tensor interaction is too strong. However, when larger spaces are used, there is a diminishing of these effects, which, in general, leads to better agreement with experiment.

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arXiv1994

Orbital and Spin Magnetic Dipole Strength in a shell model calculation with $ΔN$=$2$ excitations: $^8\mbox{Be}$

The magnetic dipole strength and energy-weighted strength distribution is calculated in $^8\mbox{Be}$, as well as the separate orbit and spin parts. All $ΔN$=$2$ excitations over and above (and including) the configuration $0s^4$$0p^4$ are included. The interaction has a central, two-body spin-orbit and a tensor part. The energy- independent and energy-weighted {\underline orbital} strength distribution is remarkably insensitive to the presence or absence of the spin-orbit or tensor interaction -not so the spin strength. The energy-weighted strength distribution can be divided into a low enegy and a high energy part. The high energy orbital part is somewhat less but close to the low energy part, in fair agreement with a prediction that they be equal by de Guerra and Zamick and by Nojarov. There is a wide plateau separating the low energy part from the high energy part.

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arXiv1994

Resistance to Collapse: The Tensor Interaction

We consider negative-parity excitations in $^4\mbox{He}$, $J^π$=$0^-$ and $1^-$ with isospin $T$=$0$ and $T$=$1$. We show tha t, in contrast to one-particle one-hole results, in a shell model diagonalization none of the above collapses to zero energy as the strength of the tensor interaction is increased.

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arXiv1993

Higher-shell corrections for systems with one and two valence nucleons: A spin-orbit and tensor interaction analysis

It is shown that when higher-shell admixtures are included for systems with two valence particles or holes, there are effects which are quite different from those for one-valence-nucleon systems. For example, for nuclei with one valence particle or hole, there is no first-order correction for the magnetic dipole moment or the Gamow-Teller transition amplitude. However for nuclei with two valence particles or holes, one can get substantial corrections. The effects of the tensor and spin-orbit interactions in core renormalization are emphasized. We find that in 6Li, the spin-orbit interaction causes the quadrupole moment of the J=1+ ground state to be positive, but the tensor interaction causes it to be negative. The G-matrices derived from realistic interactions are employed in these calculations.

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arXiv1993

Orbital M1 versus E2 strength in deformed nuclei: A new energy weighted sum rule

Within the unified model of Bohr and Mottelson we derive the following linear energy weighted sum rule for low energy orbital 1$^+$ excitations in even-even deformed nuclei $$S_{\rm LE}^{\rm lew} (M_1^{\rm orb}) \cong (6/5) ε(B(E2; 0^+_1 \rightarrow 2_1^+ K=0)/Z e^2 ^2) μ^2_N$$ with B(E2) the E2 strength for the transition from the ground state to the first excited state in the ground state rotational band, $ $ the charge r.m.s. radius squared and $ε$ the binding energy per nucleon in the nuclear ground state. It is shown that this energy weighted sum rule is in good agreement with available experimental data. The sum rule is derived using a simple ansatz for the intrinsic ground state wave function that predicts also high energy 1$^+$ strength at 2$\hbar ω$ carrying 50\% of the total $m_1$ moment of the orbital M1 operator.

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arXiv1993

Correlation between the quenching of total GT+ strength and the increase of E2 strength

Relations between the total beta+ Gamow-Teller (GT+) strength and the E2 strength are further examined. It is found that in shell-model calculations for N=Z nuclei, in which changes in deformation are induced by varying the single-particle energies, the total GT+ or GT- strength decreases monotonically with increasing values of the B(E2) from the ground state to the first excited J=2+ state. Similar trends are also seen for the double GT transition amplitude (with some exceptions) and for the spin part of the total M1 strength as a function of B(E2).

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