Purity of analog spin in isobaric analog resonances

It is shown that the position of the pole of the inverse averageS-matrix of an isolated isobaric analog resonance (IAR) is a very useful parameter, which allows one to distinguish between the weak and the strong coupling case of the finestructure distribution of the resonance. It gives also a direct measure of the purity of analog spin of the resonance. As an example the lowest IAR in²⁰⁸Bi is discussed.     

Isospin mixing matrix elements extracted from isobaric analog resonances

A compilation of isospin mixing matrix elements is provided. We restrict ourselves to results extracted from the analysis of isolated isobaric analog resonances. This amounts to collecting the published spreading widths of the resonances. A theoretical part has been added in order to make the present paper self-consistent: The spreading width is defined, the distinction between its external and internal parts is explained and the approximations are discussed that allow the extraction of the spreading width from experiment. It turns out that the spreading width does not depend on the level density of the fine structure into which the isobaric analog resonance is embedded.     

Particle-hole calculation of the isobaric analog and isovector monopole resonances

The correlated proton-particle—neutron-hole spectrum is calculated for N > Z nuclei using a Skyrme type interaction and the response function method. The basis of the calculation is a complete one-particle—one-hole space with the continuum included. As a result the distribution of the isovector monopole strength in the analog nucleus is obtained. This distribution has a narrow peak which corresponds to the isobaric analog resonance and at higher energies a broad peak which is the isovector monopole resonance. The coupling between these two states is inherent in the calculation.     

Investigation of isobaric analog resonances in 53Mn

The isobaric analog resonances in ⁵³Mn with different spins and parities are investigated by means of the ⁵²Cr(p, p), (p, p′), (p, p′γ), and (p, γ) reactions. Spectroscopic factors are derived and the experimental (p, γ) strengths are compared with theoretical single-particle estimations.     

Analog spin wave functions and spreading widths of isobaric analog resonances

The coupling of the isobaric analog state (IAS) to the giant isovector monopole state has been shown by Mekjian and Auerbach to dramatically affect the calculation of the spreading width. We show that the inclusion of this coupling is equivalent to a new definition of the IAS as an eigenstate of analog spin in which each proton radial wave function is distorted relative to the corresponding neutron radial wave functions by the central Coulomb field.     

A direct measurement of the total proton decay width of an isobaric analog state

Differential cross sections for the ²⁰⁸Pb (p, n) reaction populating the isobaric analog state (IAS) of the ²⁰⁸Pb ground state in ²⁰⁸Bi have been measured at a proton bombarding energy of 30.5 MeV. The experimental technique utilized the proton (p?) decay of the IAS to obtain neutron time-of-flight spectra. When these differential cross sections are compared to those obtained for the same reaction at 30.5 MeV using the pulsed-beam technique to obtain neutron time-of-flight spectra, the percentage of the IAS decay through p? channels is obtained. This comparison indicates that the p? decay of the IAS to the first three states of ²⁰⁷Pb accounts for almost all of the IAS width (0.97±0.28).     

E1 isobaric analogue resonances of strongly deformed nuclei in (e,e′p) reactions

The cross sections of the (e, e′p) reaction on the deformed nuclei ¹⁵⁹Tb, ¹⁶⁵Ho, ¹⁶⁹Tm, ¹⁷⁵Lu and ¹⁸¹Ta have been measured in the vicinity of the ground isobaric analogue state. Resonances corresponding to the E1 isobaric analogue states are found and displacement energies are calculated from these resonances. These energies are smaller than those obtained from proton scattering, which shows their dependence on the reaction type. The radiative widths of the E1 transitions of the isobaric analogue resonances were obtained. The ratio of these to the single-particle width calculated with the Nilsson model is order of 0.1–1 for non-spin-flip transitions and more than 10² for spin-flip transitions. These results are similar to those of the spherical nuclei ¹³⁹La, ¹⁴¹Pr, ²⁰⁷Pb and ²⁰⁹Bi.     

Elastic and inelastic scattering of polarized protons from even n=82 nuclei near isobaric analog resonances

Excitation curves for the elastic and the inelastic scattering of polarized protons on the target nuclei ¹³⁸Ba, ¹⁴⁰Ce, ¹⁴²Nd and ¹⁴⁴Sm have been measured in the energy region of prominent isobaric analog resonances. A detailed analysis of the data is presented. Definite J^π assignments are given for a number of parent analog states. Spectroscopic factors and amplitudes for configurations with the core in the ground state or in the 2₁⁺ excited state are derived from the elastic and inelastic proton decay amplitudes. They show consistency with sum rules including orthogonality conditions. Different methods for the-calculation of single particle decay widths have been applied. The qualitative agreement with present unified model calculations is remarkable; an overestimattion of the weak coupling structure, however, becomes apparent.     

Quantitative evidence of weak isospin mixing in the low-lying isobaric analog resonances in 209Bi

The excitation functions of ${}^{208}\text{Pb}\text{(}\text{p}\text{,}\text{p}{}_0\text{)}{}^{208}\text{Pb}$ have been measured in the energy range E_p = 14.2 to 17.4 MeV in 50 keV steps at θ_lab = 120°, 140° and 160°. The isobaric analog resonances of the parent states in ²⁰⁹Pb up to E_x = 2.5 MeV and the optical-model background were fit simultaneously at all energies and angles. The spreading widths and the values of a parameter β², which measures the isospin purity of the IAR, were determined for the $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{,}\text{i}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{,}\text{j}{}_{\mathrm{<mtext>15</mtext><mtext>2</mtext>}}\text{,}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, and $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ resonances. An average value of the isospin purity of β² = 66% was found.     

Stripping to analog resonances

Stripping to analog resonances is studied by expressing the DWBA cross section in terms of the resolvent operator appropriate to the system composed of the proton and the target. The resolvent operator is decomposed, by means of the Feshbach projection operator technique, into parts corresponding to the entrance channel, the analog state and the compound states. The approximation scheme is similar to that used in our previous treatment of proton scattering at an analog resonance. The complex proton form factor depends on the Green function satisfying the inhomogeneous Schrödinger equation corresponding to elastic scattering and on the Coulomb potential generated by the target. The method is applied to (³He, d) stripping to analogs in ^{93, 95, 97}Tc.     

Experimental displacement energies of isobaric analog states in the 1f72 shell

Q-values for the (p, t), (p, ³He) and (p, d) reactions for twenty-five isobaric analog states in the $\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ shell have been accurately measured. The corresponding experimental displacement energies are compared with recent model predictions.     

The decay of the 11.80 MeV isobaric analog resonance in93Tc to negative parity states in92Mo

The 2,524 keV 5^? state and 2,848 keV3^? state in⁹²Mo were excited by inelastic proton scattering going through the 11.80 MeV isobaric analog resonance in⁹³Tc. Angular distributions of the 3^?→ 2⁺ and 5^?→ 4⁺ γ-rays were measured and analyzed in order to obtain the partial waves of the outgoing protons.     

Dibaryon resonances with retarded decay

The nonstrange resonances which cannot decay in the NN, NΔ or ΔΔ channels or which can decay in these channels only with the $\text{ls}$ and tensor quark-quark interaction, are presented in the nonrelativistiv quark model with six quarks grouped in two clusters. The GCM calculation gives energies of 3203 MeV, 2540 MeV and 2814 MeV for the resonances (T = 0, S = 0, L = 0), (T = 0, S = 1, L = 1) and (T = 1, S = 0, L = 1), respectively.     

Microscopic structure of nuclei from scattering through isobaric analogue resonances

Microscopic nuclear structure information that can be reached by proton scattering through isobaric analogue resonances (IAR) is discussed, mainly within the framework of weak-coupling. The concept of isospin for unbound states is examined. A critical evaluation of the methods for extracting nuclear structure information from the experimental results (such as excitation functions, angular distributions, etc.) is given. The mass regions that are studied in detail are the Pb-region and the N = 82 neutron single-closed shell nuclei. Attention is given to the comparison between weak-coupling calculations and experimental results supporting this concept in many nuclei. Level schemes as well as proton partial decay widths and angular distributions have been calculated and compared with the existing data concerning the proton decay of IAR. The concept of generalized neutron particle-hole (GNPH) state is introduced and its occurence extensively discussed within the Pb-region and N = 82 nuclei.     

Widths of the isobaric analog state of 208Pb

Both escape and spreading widths are evaluated microscopically in a consistent framework for the isobaric analog of the ²⁰⁸Pb ground state. A TDA Green function is obtained within the space of discretized J = 0⁺ proton-particle neutron-hole configurations using the Skyrme interaction. Couplings of these configurations with continuum and more complicated configurations are included into TDA matrix elements with a form of energy dependent terms. The energy and the widths of the isobaric analog resonance are obtained as a result of the matrix diagonalization. Comparison is made of the results with the former theoretical calculations as well as experimental data.