Natural Parity Transitions Research Articles

Electron wave functions in beta-decay formulas revisited (II): Completion including recoil-order and induced currents

Abstract We present complete formulas of the allowed and first-forbidden transitions of nuclear beta decay taking into account the recoil-order and induced currents up to the next-to-leading order (NLO). The longitudinal part of the vector current is cleared away by the use of the conservation of the vector current for the multipole operators of the natural-parity transitions, which makes the effect of the meson exchange current for the vector current as small as possible. The formula is transparent enough to be applied to various beta-decay processes. As a numerical demonstration, we apply our formulas to the beta decay of a neutron-rich nucleus 160Sn. We find that the NLO corrections amount to 10–20 percent of the total decay rate, whereas the induced currents alter the rate at most by 5 percent.

Reaction mechanism for natural parity (p,p') transitions inB10

We report angular distribution measurements of the cross section, analyzing power, induced polarization, and all polarization transfer coefficients for the natural parity transitions in $^{10}\mathrm{B}$($\stackrel{\ensuremath{\rightarrow}}{p},{\stackrel{\ensuremath{\rightarrow}}{p}}^{'}){}^{10}$B at 197 MeV. All of the transitions closely follow the pattern for spin-1/2 scattering from spin-0, namely $A=P,{D}_{{\mathit{SS}}^{'}}={D}_{{\mathit{LL}}^{'}}$, and ${D}_{{\mathit{SL}}^{'}}=\ensuremath{-}{D}_{{\mathit{LS}}^{'}}$. Small deviations from ${D}_{{\mathit{NN}}^{'}}=1$ reflect spin-flip contributions to these transitions. Distorted wave impulse approximation calculations were generally successful, supporting the use of an empirical effective nucleon-nucleon interaction, the inclusion of channel-coupling in the ground state and the ${3}^{+}\ensuremath{\leftrightarrow}{4}^{+}$ transition, and the procedure of increasing the $L=2$ strength of shell-model particle-hole matrix elements to match the collective contribution to these transitions.

Spin-flip probabilities in Pb208 measured with 200 MeV protons.

Measurements using 200 MeV protons of the spin-flip probability parameter ${\mathrm{S}}_{\mathrm{NN}\ensuremath{'}}$ have been made on ${\mathrm{Pb}}^{208}$ covering an excitation energy range of 2 to 24 MeV for momentum transfers from 0.45 to 0.84 ${\mathrm{fm}}^{\ensuremath{-}1}$. These data have been compared to calculations that use random-phase-approximation wave functions in an impulse approximation model. Distortions are shown to have a large effect in the calculation of ${\mathrm{S}}_{\mathrm{NN}\ensuremath{'}}$. The calculations describe the data well and suggest that natural-parity transitions contribute significantly to the spin-flip response. A broad structure is observed near 7 MeV; calculations suggest that this structure is composed of a superposition of a number of spins and parities.

Structure phenomena in the orbiting 12c + 24Mg system

The backward-angle yield from 12C + 24Mg has been studied with the technique of inverse kinematics, using 24Mg beams with energies from 90 to 126 MeV. In the different exit channels with 5 ⩽ Z ejectile ⩽9 the Q-integrated differential cross sections dσ dθ are consistent with isotropy at 130° ⩽ θ c.m. ⩽ 165°, which is taken as signature of orbiting. The most probable exit energies in the strongly predominant even- Z channels as a function of bombarding energy give evidence for complete damping at angular momenta close to the critical ones for fusion. The results for the weakly populated odd- Z channels suggest that the conditions of damping are affected by the large negative ground-state Q-values. Structures are observed in the Q-value spectra and in the excitation functions at given Q. The former are identified with high-spin states close to the yrast lines, which are shown to be selectively populated due to the matching conditions for deep-inelastic reactions in light heavy-ion systems. An additional selectivity for natural-parity transitions gives evidence for the conservation of the dinuclear parentage. Narrow fluctuations observed in the excitation functions for fixed narrow Q-windows are attributed to the overlapping of unbound states of the intermediate complex. In the Q-integrated excitation functions these fluctuations cancel, but weak gross structure of a few MeV width remains visible. A statistical analysis of the narrow fluctuations yields coherence widths around 400 keV, corresponding to lifetimes of the intermediate dinucleus around 2 × 10 −21 s.

Selective parity transitions and dinuclear orbiting of 12C

In a spectroscopic study of the backward-angle yield from /sup 12/C+/sup 24/Mg at 3--4 times the Coulomb barrier, we find a strong preference for natural parity transitions in the excitation of close-to-yrast rotational bands. This selectivity is in strong quantitative disagreement with Hauser-Feshbach calculations for a compound-nuclear reaction and provides evidence for the conservation of the dinuclear parentage.

One- and two-step processes in natural- and unnatural-parity 208Pb( [formula omitted], t) 206Pb reaction at Ep = 22 MeV

Reaction mechanism and nuclear-structure dependence of the natural- and unnatural-parity 208Pb(p, t) 206Pb(2 +, 3 +, 4 +, 5 − and 7 −) reaction are studied by using a 22 MeV polarized proton beam. Angular distribution of the analyzing power for the second 3 +(3 2 +) transition has an opposite sign to that for the 3 1 + one and the difference is explained in terms of the j-dependence in the sequential two-step (p, d)(d, t) process. The observed analyzing powers and cross sections for the two 3 + transitions are reproduced by the finite-range first- and second-order DWBA calculation. Two-step analysis is necessary to explain the variety of angular distributions of the analyzing powers for the natural-parity transitions. Microscopic analysis in terms of the one- and two-step (p, t) calculation is made for the transitions to the 2 1–5 +, 4 1–3 +, 5 1, 2 − and 7 1 − states in 206Pb. The calculation reproduces the absolute values of the observed cross sections within a factor of 2.

The role of the sequential-transfer process in natural-parity transitions in the 208Pb(p, t) 206Pb reaction

Data for natural-parity transitions in the 208Pb(p, t) 206Pb reaction measured at E p = 20 and 50.5 MeV plus existing data at E p = 26.2, 35, 40 and 80 MeV have been analysed in zero-range as well as exact finite-range DWBA. The extracted enhancement factors exhibit a similar strong dependence on the bombarding energy, with a relative minimum at E p = 35 MeV. It is demonstrated that this energy dependence is largely removed when sequential transfer (p, d)(d, t) is included in the calculations, except at E p = 35 MeV. At this bombarding energy a phasing problem between the direct- and sequential-transfer amplitudes is encountered which seems to be related to resonances in the intermediate deuteron channel.

Pion inelastic scattering to the low-lying excited states ofLi6

The excitation function for ${\ensuremath{\pi}}^{+}$ inelastic scattering to the ${0}^{+}$, $T=1$, 3.563-MeV level of $^{6}\mathrm{Li}$ has been measured at a constant momentum transfer $q\ensuremath{\simeq}109$ MeV/c for incident pion energies from 100 to 260 MeV. Although the differential cross sections extracted for the natural-parity transitions to the ${3}^{+}$, $T=0$, 2.185-MeV and ${2}^{+}$, $T=0$, 4.25-MeV levels are well reproduced within the framework of the distorted-wave impulse approximation, distorted-wave impulse approximation calculations fail to reproduce the anomalous excitation function observed for the transition to the 3.563-MeV level. The shape of the 3.563-MeV excitation function is similar to that previously observed for ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ inelastic scattering to the ${1}^{+}$, $T=1$, 15.11-MeV state of $^{12}\mathrm{C}$ [C. L. Morris et al., Phys. Lett. 108B, 172 (1982)]. The same mechanism may be responsible for the observed excitation functions of both $\ensuremath{\Delta}S=\ensuremath{\Delta}T=1$ transitions. A possible mechanism is the previously proposed direct excitation of $\ensuremath{\Delta}$-particle-nucleon-hole ($\ensuremath{\Delta}\ensuremath{-}h$) components in the wave functions.

Inelastic scattering of 40 MeV protons fromMg24. II. Microscopic calculations for positive parity states

Proton inelastic scattering data at 40 MeV bombarding energy are compared to microscopic distorted-wave Born-approximation calculations for positive parity states in $^{24}\mathrm{Mg}$ utilizing shell-model wave functions spanning the full $2s1d$ shell basis. Both empirical forces and forces derived from free nucleon-nucleon potentials are used in the calculations. Except for four transitions for which strong coupling effects are evident, the agreement between theory and experiment is quite good. Enhancement factors extracted for the natural parity transitions are consistent with the effective charges obtained from electromagnetic transition rates. Levels corresponding to the giant $M1$ resonance in $^{24}\mathrm{Mg}$ have been resolved in the present experiment. The fact that the renormalization factor between theory and experiment is close to unity for the 10.713 MeV 1+; $T=1$ state indicates that little or no renormalization of the two-body force is necessary for this inelastic transition. It is argued that little renormalization is also involved for magnetic-type inelastic transitions of multi polarities higher than $M1$.

Two-neutron pickup strengths on the even lead isotopes the transition from single-particle to “collective”

The (p, t) reaction on 208Pb, 206Pb, and 204Pb has been studied with 35 MeV protons. It is observed that the L = 0 ground-state cross section rapidly increases as one changes targets from 208Pb to 206Pb to 204Pb while the cross section for other natural-parity transitions decreases. The observed cross sections are compared with predictions of the shell model and the pairing-vibration model. Both models are seen to describe some features of the data.