Mirror Transitions Research Articles

Remarks on the occasion of the 25th anniversary of the discovery of isobaric­analog states

I am honored to have this opportunity to recognize the man who started this charge-exchange business. He is, of course, John Anderson. A few days ago our workshop chairman, Peter Jackson, called me and reminded me that this is the 25th anniversary of the discovery of isobaric-analog states (IAS). He asked me to say a few appropriate words. Roughly 25 years ago, John Anderson, the late Calvin Wong, John McClure, and Stewart Bloom made an interesting discovery (1). In fact, it was so interesting that it has not yet been superseded by a more important discovery of nuclear structure. John and his colleagues had set out to measure the systematics of nuclear temperatures. They were to look at the spectra of evaporated neutrons from compound nuclei created by proton bombardment of various targets. The evaporation spectra should be smooth functions of energy. The smooth functions were there, but there was a sharp peak superimposed, as shown in Fig. 1 . (2). No known physical phenomenon could produce the sharp peak, so it had to be an artifact of the electronics. However, John and his colleagues convinced themselves that the time-to-pulse-height converters were working right. Well then, it had to be a contaminant in the target. Sharp peaks had 5 1 been seen for isospin mirror transitions, but this target, ??VZK, had five excess neutrons, so there could not be a mirror transition. The prevailing dogma was that isotopic spin, as it was then called, was a bad quantum number because the Coulomb force was so strong. Well, John and his colleagues set about to calculate the Z of the contaminant mirror transition that would put the sharp peak at the observed energy. They found Z = 23, 600 TARGET I

Neutron transition density for the lowest 2 + state of 18O

Scattering of 135 MeV protons is used to fit an expansion in radial basis functions of the neutron transition density for the lowest 2 + state of 18O. The narrow error envelope shows good radial sensitivity. The results are consistent with electromagnetic decay data for the mirror transition in 18Ne.

Neutron and proton polarisation charges from E2 mirror transitions

Abstract A review of sd-shell data relevant to a determination of the E2 effective charge is presented. A best fit is obtained assuming a linear dependence of the isoscalar effective charge on mass number, consistent with the predictions of the schematic model. Theory and experiment also agree in yielding a ratio of neutron to proton polarisation charges close to two.

Measurements of Gamow-Teller strength distributions in masses 13 and 15.

The differenctial cross section and the transverse spin-flip probability have been measured for the dominant transitions in $^{13}\mathrm{C}$(p,n${)\mathrm{}}^{13}$N and $^{15}$N(p,n${)\mathrm{}}^{15}$O at ${\mathrm{E}}_{\mathrm{p}}$=160 MeV. The Gamow-Teller transition strengths deduced from the data show that the major ${(1/2)}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}${(3/2)}^{\mathrm{\ensuremath{-}}}$ transitions are strongly quenched relative to the ${(1/2)}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}${(1/2)}^{\mathrm{\ensuremath{-}}}$ mirror transitions, in strong disagreement with simple shell-model expectations.

The 19F(p, n) 19Ne and 39K(p, n) 39Ca reactions at intermediate energies and quenching of the Gamow-Teller strength

The (p, n) reactions on 19F and 39K targets have been studied at 120 MeV and 160 MeV using the Indiana University Cyclotron time-of-flight facility. States up to 12 MeV excitation energy have been observed and angular distributions for these neutron groups are presented. The ground-state mirror transitions have accurately measured ft values. This information is used to normalize the zero-degree energy spectra to a scale of Gamow-Teller (GT) transition probability to obtain GT strenghts to excited states. The experimental sum GT strengths are smaller than the sum-rule-limit values showing strong evidence for GT quenching.

The mirror transition of the [formula omitted] nucleus 59Zn

The mirror transition of the T z = − 1 2 nucleus 59Zn was studied by using an isotope separator on-line. The half-life and E max β + were measured to be 182.0 ± 1.8 ms and 8100 ± 100 keV, respectively. The ft values and the Gamow-Teller matrix elements to the low-lying states of 59Cu were determined and compared with the shell-model values. The masses of neutron-deficient Zn isotopes were calculated from the Kelson-Garvey mass relation.

Lifetime measurements of levels in 26Si and the ratio of neutron to proton transition amplitudes for mirror nuclei

The mean lifetimes of the 1796, 2784, 3333 and 4138 keV levels of 26Si have been measured using the Doppler shift attenuation method. The ratios of neutron to proton transition matrix elements determined from these data and additional data from mirror transitions in 26Mg are compared with recent data from inelastic pion scattering and with shell model calculations. The isoscalar strenghts are compared with α-scattering data.

Beta decay of12B and12N to the first excited state of12C (4.44 MeV)

The branching ratios of the beta-decay of12B and12N to the 4.44 MeV state in12C were determined by (βγ-coincidences to be (1.182±0.019)% and (1.898±0.032)% of the total rate, resp. This givesft−=(1.407±0.023) · 105 s andft+=(1.406±0.024) · 105 s. For theft-asymmetryδ=(ft+/ft−)−1 the valueδ=−(1±14) · 10−3 was obtained. This is in contrast to other GT mirror transitions which show positiveδ of a few percent.

Étude des États excités du 33Cl à l′aide de la réaction 32S(p, γ)33Cl

Abstract Energies and strengths of resonances of the 32S(p, γ)33Cl reaction were determined in the range Ep = 0.4 − 2.6 MeV. Three new resonances were observed respectively at Ep = 1588, 1748, 1880 keV and the doublet of resonances at Ep ≈ 1900 keV was clearly shown. The (p, γ) strengths of resonances at Ep = 422, 580, 588, 721 and 2577 keV were measured with a 80 cm3 Ge(li) detector. The Q-value of this reaction and the energies, γ-ray branchings and mean lifetimes of levels were determined. The spins and parities of the Ex = 2.35, 3.82, 3.97, 3.98, 4.78 MeV levels have been measured. A comparison of γ-ray transition strengths with mirror transitions and with model predictions is made.

Asymmetry of MirrorγDecays inC13andN13

An explanation is offered for the large difference in $B(E1)$ values of mirror transitions from ${\mathrm{\textonehalf{}}}^{+}$ state to the ground state, based on the difference in binding energy of the ${\mathrm{\textonehalf{}}}^{+}$ states. The binding energy determines the degree of coupling of the positive parity nucleon to the deformed $^{12}\mathrm{C}$ core, which in turn affects the $B(E1)$ value. The experimental asymmetry can be satisfied with a small change of the wave function.

Mechanism of (p, t) and (p,He3) reactions by the analysis of the energy dependence of mirror transitions

The reactions $^{13}\mathrm{C}(p, t)^{11}\mathrm{C}$, $^{13}\mathrm{C}(p, ^{3}\mathrm{He})^{11}\mathrm{B}$, $^{16}\mathrm{O}(p, t)^{14}\mathrm{O}$, and $^{16}\mathrm{O}(p, ^{3}\mathrm{He})^{14}\mathrm{N}$ have been studied at several incident energies between 24 and 44 MeV. Previous results on the $^{15}\mathrm{N}(p, t)^{13}\mathrm{N}$ and $^{15}\mathrm{N}(p, ^{3}\mathrm{He})^{13}\mathrm{C}$ reactions are also considered in the analysis. The energy dependence of cross section ratios for mirror transitions evidences that these reactions cannot be described below 35-40 MeV simply as a direct two-nucleon pickup. The values for spin and isospin dependent terms in the effective interactions obtained from a distorted-wave Born-approximation analysis differ from those used in shell model calculations and in microscopic analyses of inelastic scattering.

The second-class current problem in nuclear beta decay

Taking into account in a simple but non-trivial way both off-mass-shell and meson-exchange effects, we calculate the second-class current (scc) contribution to asymmetries in nuclear mirror Gamow-Teller decays. No assumptions on the divergence of the scc are made but the previous result obtained for a divergenceless current is recovered straightforwardly from our formula. Of the plethora of parameters that can be brought in for a current with non-vanishing divergence, we confine ourselves to the minimum number (two) which still renders our calculation sufficiently realistic while retaining its predictive power. The two parameters - one associated with the off-shell phenomenon and the other with meson-exchange current - are determined from two pieces of experimental data on the A = 8 system (the averaged asymmetry δ obtainable from the total decay rates and the slope in the plot of δ versus the energy release) and predictions are made for the scc effects in other mirror transitions. On the average the expected scc contribution to mirror asymmetry δ is 2 to 5%, for both even- and odd- A nuclei. We reach the same conclusion as Wilkinson that the large residual asymmetry (≳10%) left unaccounted in odd- A nuclei must be nuclear in origin. The fundamental nucleon pseudotensor coupling constant implied by this result is still of the same order (∼1/ M, where M is nucleon mass) as that of the weak magnetism or pseudoscalar terms. In the absence of kinematic suppression, this could induce large effects. Thus the ω-decay into π ±e −+ ν is expected to be as fast as any allowed first-class decay of a meson with comparable mass. The asymmetries in various correlation experiments (i.e. eη correlation and up-down asymmetry with respect to nuclear spin polarization) are predicted to be large enough to be measurable. We make a detailed analysis on whether, as conjectured by Lipkin, the meson-exchange current can build up coherently for large nuclei. The conclusion drawn therefrom is that such an enhancement does not materialize.

Induced-Tensor Interaction in Weak Processes

The nonrelativistic impulse approximation for the induced-tensor interaction has been analyzed in detail. $\mathrm{ft}$ values for mirror transitions have been calculated using electron Coulomb wave functions for the extended charge distribution and introducing higher-order corrections. 14 angular $\ensuremath{\beta}\ensuremath{-}\ensuremath{\gamma}$ correlations, the $\ensuremath{\beta}$ transition being allowed, have been analyzed, showing that this process is sensitive to the presence of the induced-tensor interaction. The amount of information about the induced tensor at present obtainable from circular $\ensuremath{\gamma}$ polarization in nuclear transitions has been investigated. A limit on the induced-tensor coupling constant has been obtained which does not contradict the evidence based on $\mathrm{ft}$ values. $\ensuremath{\beta}\ensuremath{-}\ensuremath{\gamma}$ angular correlations seem to yield evidence for the weak-magnetism term, while not excluding the existence of the induced tensor.

Mirror asymmetry in Gamow-Teller transitions of large ft value

Abstract The several single-nucleon wave functions appropriate to the several parent states of a β-decaying nucleus are different in that they must reflect the several separation energies. These differences engender differences between the overlap integrals that enter into the β-transition amplitudes which will therefore themselves differ as between the negaton- and positon-emitting members of an isobaric mirror since the separation energies differ on the two sides of the mirror. The question is asked as to how large this effect may be in cases where, because of strong cancellation between parents, the ft value is large and so where this asymmetry due to binding energy differences will be largest. The question is answered via a Monte Carlo approach: it is shown that large log ft value differences may indeed be expected but that the effect is not large enough to account for the differences found in the A = 14 and 32 systems. This conclusion agrees with that made earlier in relation to the small ft value differences found between mirror transitions of normal ft value.

First-forbidden non-unique β-transitions and mirror comparisons in light nuclei

Abstract Shape factors and longitudinal polarisations are calculated for first-forbidden non-unique β-decays between spin - 1 2 states in masses A = 15 and A = 17. The nuclear matrix elements are evaluated using particle-hole models. Core-polarisation corrections are included to first order in perturbation theory. A characteristic hindrance becomes evident, which reduces all nuclear matrix elements in magnitude with the electric-dipole matrix element being particularly retarded. A consequence is that the energy spectrum has very nearly the allowed shape, contrary to expectations for high-energy decays in light nuclei. It is argued, however, that nuclear matrix elements may be determined from experimental shape factors and in particular that improved accuracy results from the comparison of mirror transitions under the assumptions of strict mirror symmetry. On the other hand, longitudinal polarisations are shown to be very insensitive to matrix elements in high-energy, light-nuclei situations.

Gamma-Ray Transitions inA=35Nuclei

The mean lifetime of the 1.99-MeV ${\frac{7}{2}}^{\ensuremath{-}}$ level of ${\mathrm{S}}^{35}$ was determined by a measurement of the delayed coincidence between protons and $\ensuremath{\gamma}$ rays in the reaction ${\mathrm{S}}^{34}(d,p\ensuremath{\gamma}){\mathrm{S}}^{35}$ at ${E}_{d}=4.48$ MeV, with the result ${\ensuremath{\tau}}_{m}=1.47\ifmmode\pm\else\textpm\fi{}0.07$ nsec. The $\ensuremath{\gamma}$ decay of the ${\frac{7}{2}}^{\ensuremath{-}}$, $T=\frac{3}{2}$ analog of this level at ${E}_{x}=7.55$ MeV in ${\mathrm{Cl}}^{35}$ was examined in detail with large-volume Ge(Li) detectors and Ge(Li)-NaI(Tl) coincidence techniques. The $\ensuremath{\gamma}$-ray spectra obtained at the analog state, which appears as a well-known resonance at ${E}_{p}=1211$ keV in the reaction ${\mathrm{S}}^{34}(p,\ensuremath{\gamma}){\mathrm{Cl}}^{35}$, revealed the presence of several previously unknown transitions in addition to the known strong analog-to-antianalog $M1$ transition to the ${\frac{7}{2}}^{\ensuremath{-}}$, $T=\frac{1}{2}$ level at 3.16 MeV. Examples are a crossover $M2$ transition from the analog resonance to the ${\frac{3}{2}}^{+}$ ground state of ${\mathrm{Cl}}^{35}$ with a strength of 3.0 \ifmmode\pm\else\textpm\fi{} 0.8 Weisskopf units, a mixed $E1\ensuremath{-}M2$ transition ($\ensuremath{\delta}=0.44\ifmmode\pm\else\textpm\fi{}0.12$) from the ${\frac{7}{2}}^{\ensuremath{-}}$ antianalog state to the ${\frac{5}{2}}^{+}$ level at 1.76 MeV, and a 160-keV transition between the antianalog state and the ${\frac{5}{2}}^{+}$ level at 3.00 MeV. Weak transitions which can be interpreted as members of cascades through levels in the region ${E}_{x}=4.3\ensuremath{-}5.7$ MeV were also identified. It is shown that the $M1$, $E2$, $M2$, and $E3$ strengths of transitions connecting members of the system of parent, analog, antianalog, and ground states can be accurately reproduced by a simple model based upon an inert ${\mathrm{S}}^{32}$ core with active nucleons in the ${d}_{\frac{3}{2}}$ and ${f}_{\frac{7}{2}}$ orbits, with bare-nucleon $g$ factors for the magnetic transitions, and with reasonable effective charges for the electric transitions. The wave functions for the ${\frac{7}{2}}^{\ensuremath{-}}$ levels derived from this model are used to predict strengths of mirror transitions in ${\mathrm{Ar}}^{35}$ and ${\mathrm{K}}^{35}$.

Angular correlation studies of electromagnetic transitions following the 16O(τ, α)15O reaction

Abstract A particle-gamma angular correlation coincidence technique enabling the measurement of 0° coincidences was used to study levels in 15 O at 5.24 MeV (J π = 5 2 + ) , 6.18 MeV (J π = 3 2 − ) , 6.79 MeV (J π = 3 2 + ) and 6.86 MeV (J π = 5 2 + ) . The multipole mixing ratios of the de-excitation γ-rays were determined as the following: x (5.24→ 0) = +0.08±0.08 an E3/M2 mixture; x (6.86 → 5.24) = +0.04±0.03, an E2/M1 mixture; x (6.79 → 0) = −0.02±0.02, an M2/E1 mixture and x (6.18 → 0) = −0.121 ±0.008 an E2/M1 mixture. The latter value is to be compared with x (( E 2/ M 1) = +0.13 ±0.02 for the mirror 6.323 MeV transition in 15 N indicating |x( 15 O )| ≦ |x( 15 N )| contrary to previous findings (10). The results obtained, together with those corresponding to mirror transitions in 15 N are compared with recent IPM and core polarization theoretical investigations.

Mirror transitions and second class currents

Theoretical implications of observed mirror asymmetry in nuclear beta decay are examined, taking into account CP violation and internal symmetries. The second class induced tensor current is shown not to be responsible for the observed asymmetry, which must be the result of multinucleon or meson exchange effects. The result is general and holds for all values of momentum transfer. Possible two nucleon transitions are discussed. Mirror asymmetry in the Σ− Λ decay cannot be produced by SU(3) octet currents or single quark currents in the quark model even if such second class currents exist.

Gamma-ray mixing ratios in mirror nuclei

A review of the E2/M1 mixing ratios of corresponding γ-ray transitions in sd-shell mirror nuclei, shows that for the 20 pairs of mirror transitions for which the mixing ratios are known to differ significantly from zero (i) the mixing ratios have opposite sign, and (ii) the ratio of the absolute values is remarkably close to unity.

Nuclear Lifetime of theNe19275-keV Level

The mean life of the 275-keV second excited state of ${\mathrm{Ne}}^{19}$ was measured to be 61.4 \ifmmode\pm\else\textpm\fi{} 3.0 psec. The ${\mathrm{He}}^{3}({\mathrm{Ne}}^{20},\ensuremath{\alpha}){\mathrm{Ne}}^{19}$ reaction and the gas-target recoil-distance technique were used. The 275-keV state decays by $E1$ emission to the ground state. The strength of this $E1$ transition is equal within errors to that of the mirror transition in ${\mathrm{F}}^{19}$. This result is discussed.