Calculation Of Effective Interaction Research Articles

Two-particle ladder diagrams and double-counting in effective interaction calculations

It is shown that including the two-particle ladder diagrams, computed with the Barrett, Hewitt, McCarthy G matrix elements at a starting energy of 47 MeV and for intermediate excitations of 2ℏΩ, in the perturbation expansion for the effective two-body interaction in mass-18 nuclei involves a double-counting of roughly 42%. It is argued by comparison that the double-counting should be roughly the same when the Kuo G matrix elements are used.

Effective interaction calculations for nuclei of mass 6 to 9

Shell model calculations using the effective interaction approach of Talmi are reported for normal parity states in nuclei of mass number 6–9. To fit simultaneously the energies of levels in these nuclei, energy shifts of ground state rotational bands in 8 Be and 9 Be are introduced. These shifts have their origin in the deformations of nuclei. The obtained matrix elements fit the data better than those of earlier authors, and resemble the matrix elements obtained from realistic interactions such as the Hamada-Johnston potential. Theoretical predictions are compared with new experimental data. M1 radiative widths, log ft values, and spectroscopic factors for single- and two-nucleon transfers are given to help in the interpretation of new data. The need for carrying out more calculations for 1p shell nuclei with realistic forces is discussed.

Effective-Interaction Calculation on the Energy Spectra of1f−2pNuclei. I

The energy spectra of normal-parity states of Ni isotopes are studied in the conventional shell model. The effective two-body interactions are determined by a least-squares fit between the calculated and observed low-lying energy levels. The agreement between the experimental and calculated energy spectra is quite remarkable. Single-nucleon spectroscopic factors for some low-lying states of odd-mass Ni isotopes are calculated. The resulting spectroscopic factors are similar to those calculated in other effective interaction calculations.

A phenomenological effective two-body interaction for calcium isotopes

The 1]~-2pg shell has long been one of the most studied nuclear regions. Recently there has been an extensive effective-interaction calculation on calcium isotopes by F~I)~MAN~ and PITTnL (1). The single set of matrix elements given by them has a good convergence and appears to reproduce the energy spectra, (t,p) strengths and single-neutron spectroscopic factors with reasonable agreement. Moreover, the /~pg matrix elements have the desh'ed feature of repulsion on the average. This is in agreement with the findings obtained by analysing the data from (3He, d) and (d, p) measurements in this shell (~). These matrix elements, derived from Hamada-Johnston potential (a), are, however, attractive on the average. The effective-interaction method in the framework of the shell model has the disadvantage that one cannot use a large configuration space in such calculations. Then the number of variable two-particle matrix elements increases drastically and the method fails. Even in a reasonable configuration space, the two-particle matrix elements obtained from the least-squares fit to the experimental binding energies and level energies of calcium isotopes have large statistical errors (a-e), when all the required two-particle matrix elements are allowed to vary. On the other hand, a large configuration space can be used with a phenomenological effective two-body interaction with a few adjustable parameters. The wave functions thus obtained, in view of greater configurational freedom, are more realistic than those obtained by the effective-interaction method. But it is difficult to get detailed quanti tat ive fit to the binding energies and level energies like the effective-interaction method because there are only a few adjustable parameters in a phenomenological force. So an initial test of a phenomenological residual twobody interaction is to reproduce the matrix elements obtained by the effective-interaction method to get a good description of the experimental data.

Decay scheme of 2.71 h 92Sr

Abstract Gamma rays emitted in the decay of 2.71 h 92Sr have been investigated with a Ge(Li) detector. Sources were prepared by separating Sr from fission products. A total of 10 γ-rays were attributed to the decay of 92Sr in a complex spectra with interferences from 91Sr and 92Y. Gamma-gamma coincidences in the decay of 92Sr were observed with a NaI(Tl)Ge(Li) setup. The decay scheme of 92Sr was constructed, involving placement of 8 of the γ-rays emitted between 92Y excited states at 241.4, 892.8, 953.3 and 1383.9 keV. The observed level structure is compared with previously reported predictions based on effective interaction calculations. The value for the half-life of 92Sr was determined to be 2.71 ± 0.01 h.

The 7Li( 3He, d) 8Be and 7Li( 3He, p) 9Be reactions

Angular distributions for the reaction 7Li( 3He, d) to the 8Be ground state and first excited state (2.90 MeV) were measured at 10 MeV, and distorted wave stripping calculations were made. Spectroscopic factors were deduced and are in fair agreement with those obtained from the effective-interaction calculations of Cohen and Kurath. Angular distributions for the reaction 7Li( 3He, p) to the ground and first three excited states of 9Be(1.67, 2.43, and 3.03 MeV) were measured at 10 MeV. DWBA double-stripping calculations do not predict the observed angular distributions.

Toward the calculation of effective interactions in adsorbed helium submonolayers

Toward the calculation of effective interactions in adsorbed helium submonolayers

Two-nucleon transfer in the 1p shell

Two-nucleon c.f.p. are given for the 1p shell, based on an earlier effective-interaction calculation. Magnitudes are also given which indicate the strength expected for two-nucleon transfer reactions.

Proton pick-up from the 2s-1d and 1p shells of 32S

Energy spectra and angular distributions of 3He particles from the 32S(d, 3He) 31P reaction have been measured at an incident energy of 52 MeV. A total of 15 levels has been observed upto an excitation energy of 10 MeV. A yet unknown 1 2 + level at E X = 6.41 ± 0.06 MeV has been observed. The whole 1 d 3 2 strength is concentrated in one single state while the 2 s 1 2 and especially the 1 d 5 2 strengths are split into several levels. The spectroscopic factors of positive parity states agree fairly well with recent shell model calculations. As predicted by an effective interaction calculation, 1p hole states have been observed at an energy much lower than expected from an (e, e'p) experiment. Angular shifts between measured and calculated angular distributions have been found to be of the type of recently reported shell effects. The observed forward angle j-effect fits perfectly into this concept.

The levels of 91Y from the decay of 91Sr

Abstract The gamma rays emitted in the decay of 91Sr have been studied by Ge(Li) singles and NaI(Tl) coincidence spectrometry, and energies and absolute intensities of 35 transitions have been determined. A decay scheme is proposed involving 91Y excited states at 555.6, 652.9, 925.8, 1186.9, 1305.4, 1473.7, 1545.9, 1580.0, 1980.4, 2066.7, 2206.9, 2279.4 and 2572 keV. The results of this experiment are combined with the direct reaction data of other investigators to assign spins and parities. The observed level structure is compared with previously reported predictions based on effective interaction calculations.

Decay Scheme of the 23-minCu60with High-Resolution Ge(Li) Detectors

The decay of the 23-min $^{60}\mathrm{Cu}$ has been investigated with the use of Ge(Li) and NaI(Tl) $\ensuremath{\gamma}$-ray detectors. Coincidence relationships among the $\ensuremath{\gamma}$ rays were established in $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidence experiments. It was concluded that the decay of the 23-min $^{60}\mathrm{Cu}$ populates levels at 1332.4, 2158.8, 2284.4, 2505.6, 2626.0, 3124.2, 3194.2, 3269.3, 3393.4, 3735.8, 4003.4, 4022, 4078.6, 4317, 4494, 4548, and 4573 keV. A number of transitions not reported previously have been observed and assigned in the decay scheme. The levels populated in the proposed decay scheme have been previously reported from studies of the $^{60}\mathrm{Cu}$ decay and from nuclear-reaction spectroscopic studies. From $log\mathrm{ft}$ values and $\ensuremath{\gamma}$-ray information, many spin assignments have been made. The levels are compared with the results of recent calculations on current models for the nucleus. No evidence is found for a ${0}^{+}$ state at about 2.9 MeV as predicted by the effective-interaction calculations based on the shell model.

Lifetimes of Levels inA=10Nuclei

The Doppler-shift attenuation method was used to obtain the following mean lifetimes (in psec) for the indicated nuclear levels: $^{10}\mathrm{C}$(3.36), $\ensuremath{\tau}=0.155\ifmmode\pm\else\textpm\fi{}0.025$; $^{10}\mathrm{B}$(3.59), $\ensuremath{\tau}=0.150\ifmmode\pm\else\textpm\fi{}0.015$; $^{10}\mathrm{Be}$(3.37), $\ensuremath{\tau}=0.189\ifmmode\pm\else\textpm\fi{}0.020$; $^{10}\mathrm{B}$(2.15), $\ensuremath{\tau}={{2.7}_{\ensuremath{-}0.4}}^{+0.5}$. A limit of $\ensuremath{\tau}l30$ fsec is obtained for $^{10}\mathrm{B}$(1.74), which is a factor of 8 greater than, and therefore consistent with, the lifetime computed from the analog $\ensuremath{\beta}$ decay of $^{10}\mathrm{C}$. Transition strengths obtained from the $^{10}\mathrm{B}$(2.15) and $^{10}\mathrm{B}$(3.59) lifetimes are in good agreement with the effective-interaction calculations of Cohen and Kurath, as modified by Warburton et al. The $^{10}\mathrm{C}$(3.36) and $^{10}\mathrm{Be}$(3.37) states decay by analog $E2$ transitions: ${2}^{+}$, $T=1\ensuremath{\rightarrow}{0}^{+}$, $T=1$, with ${T}_{z}=\ifmmode\pm\else\textpm\fi{}1$, whose strengths are well described by calculations of Kurath's for an effective charge ${\ensuremath{\epsilon}}_{n}={\ensuremath{\epsilon}}_{p}=0.5$. An upper limit was obtained for the corresponding transition 5.17 \ensuremath{\rightarrow} 1.74 in $^{10}\mathrm{B}({T}_{z}=0)$ which is consistent (factor of 4 greater) with the analog strengths observed in the ${T}_{z}=\ifmmode\pm\else\textpm\fi{}1$ nuclei.

The 1p neutron pick-up strengths in the reaction 13C(p, d) 12C

Excited states up to about 18 MeV in 12C have been investigated with the 13C(p,d) 12C reaction. It was found that five states (ground, 0 +, T=0; 4.43 MeV, 2 +, T=0; 12.71 MeV, 1 +, T=0; 15.11 MeV, 1 +, T=1 and 16.11 MeV, 2 +, T=1 almost exhaust the available pick-up strength. Spectroscopic factors for these states extracted from a DWBA analysis with the usual separation energy procedure gave good agreement with the prediction of the effective interaction calculation by Cohen and Kurath.

Decay of 94Tc isomers into the levels of 94Mo

The energy levels in 94Mo have been investigated from the decay of 94Tc isomers using Ge(Li) and NaI(Tl) detectors. The energies of the gamma rays in keV (and relative intensities) from the decay of 52 min 94mTc are 870.9(100), 993.1(2.6), 1196.3(0.9), 1522.0(5.9) 1868.8(5.8), 2393.0(0.6), 2530.0(0.7), 2740.0(3.8), 3129.2(1.2) and 3793.5(0.1). Gamma-ray energies (and transition intensities) observed in the decay of 5 h 94gTc are 449.0(27), 531.6(1.2), 702.6(100), 742.0(1.1), 849.7(100), 870.9(100), 916.2(6.8), 1509.7(0.7), 1591.8(2.4) and 1764.6(0.2). An angular correlation measurement indicated the presence of a second 2 + state. The results are in partial agreement with the effective interaction calculations of Bhatt and Ball and of Vervier.

Shell-model and deformed states in oxygen isotopes

The energies and some other properties of low-lying levels in the oxygen isotopes are studied in the frame of a model including shell model and deformed states, as well as the interplay among them. The calculations are performed using the effective interaction method, and very good agreement with experiment is obtained. The results are compared with previous effective interaction calculations, and also with the predictions of phenomenological forces. Particular attention is given to the determination of the parameters and unperturbed positions of the deformed states. It is concluded that the influence of the deformed states is important in 18O, but their influence in 19O and 20O is small.

Effective interaction calculations of energy levels and wave functions in the nuclear 1p shell

The effective interaction method is applied to the lp shell in intermediate coupling in nuclei from He 5 to O 16. No assumption is made on the form of the forces or the potential well. We arrive at a fixed set of two-body matrix elements of the effective interaction which reproduces all total (binding) energies of low-lying energy levels for 8 ≦ A ≦ 16. We also obtain the wave functions of the levels considered. The agreement with experiment in the present work is in many instances an improvement upon the work of Kurath. This shows that the postulation of a specific form of the interaction is a rather severe restriction. Since absolute energy values are obtained in the present method, it is possible to make predictions on the stability of nuclei so far undetected. Finally, the situation regarding nuclei with A < 8 is discussed.