Mirror Energy Differences Research Articles

Mirror energy differences of2s1/2single-particle states: Masses of10N and13F

I have examined mirror energy differences between 2${s}_{1/2}$ states in neutron-excess nuclei with $N$ $=$ 7 and 9 and their proton-excess mirrors having $Z$ $=$ 7 and 9. I find they can be fitted by a simple expression, which I then use to predict the masses of ${}^{10}$N and ${}^{13}$F.

γ-ray spectroscopy of theA=23,T=1/2nuclei23Na and23Mg: High-spin states, mirror symmetry, and applications to nuclear astrophysical reaction rates

Background: Obtaining reaction rates for nuclear astrophysics applications is often limited by the availability of radioactive beams. Indirect techniques to establish reaction rates often rely heavily on the properties of excited states inferred from mirror symmetry arguments. Mirror energy differences can depend sensitively on nuclear structure effects.Purpose: The present work sets out to establish a detailed comparison of mirror symmetry in the $A=23$, $T=1/2$ mirror nuclei ${}^{23}$Na and ${}^{23}$Mg both to high spin, and high excitation energy, including beyond the proton threshold. These data can be used to benchmark state-of-the-art shell-model calculations of these nuclei.Methods: Excited states in ${}^{23}$Na and ${}^{23}$Mg were populated using the ${}^{12}$C(${}^{12}$C,$p$) and ${}^{12}$C(${}^{12}$C,$n$) reactions at beam energies of 16 and 22 MeV, and their resulting $\ensuremath{\gamma}$ decay was measured with Gammasphere.Results: Level schemes for ${}^{23}$Na and ${}^{23}$Mg have been considerably extended; highly excited structures have been found in ${}^{23}$Na, as well as their counterparts in ${}^{23}$Mg for previously known rotational structures in ${}^{23}$Na. Mirror symmetry has been investigated up to an excitation energy of 8 MeV and spin-parity of 13/2${}^{+}$. Excited states in the region above the proton threshold have been studied in both nuclei.Conclusions: A detailed exploration of mirror symmetry has been performed which heavily constrains expectations as to how mirror energy differences should evolve for different structures. Agreement with shell-model calculations provides confidence in using such estimations where real data are absent.

Exotic structure and decay of medium mass nuclei near the drip lines

Nuclei at or near the N=Z line are of particular interest as micro-laboratory for fundamental effects. The simulation of many astrophysical objects requires the knowledge of properties and decay rates of nuclei near the drip lines. The structure and dynamics of proton-rich A70 nuclei and neutron-rich A100 nuclei are influenced by shape coexistence and mixing. A realistic description of shape coexistence phenomena requires beyond-mean-field approaches. Results concerning the self-consistent description of exotic phenomena including anomalies in mirror energy differences of proton-rich nuclei, triple shape coexistence in neutron-rich N=58 Sr and Zr isotopes as well as Gamow-Teller β-decay strength distributions, half-lives, and β- delayed neutron emission probabilities of neutron-rich nuclei in the A100 mass region obtained in the frame of the complex Excited Vampir model using realistic effective interactions in large model spaces are presented.

Systematic behavior of mirror energy differences for [formula omitted] nuclei and the mass of 15Ne

I use a simple model to parameterize mirror energy differences for several nuclei with N=8 or 10 and their mirrors with Z=8 or 10. I then use the results of the fit to predict the energy of the ground state of the unbound nucleus 15Ne: E2p=2.68(24) MeV.

Isospin symmetry in the odd-odd mirror nuclei44V/44Sc

Excited states in the $N=Z\ensuremath{-}2$ nucleus ${}^{44}$V have been observed for the first time. The states have been identified through particle-$\ensuremath{\gamma}$-$\ensuremath{\gamma}$ coincidence relationships and comparison with analog states in the mirror nucleus ${}^{44}$Sc. Mirror energy differences have been extracted and compared to state-of-the-art shell-model calculations which include charge-symmetry-breaking forces. Observed decay pattern asymmetries between the mirror pair are discussed in terms of core excitations, electromagnetic spin-orbit effects and isospin mixing.

Isospin symmetry breaking at high spins in the mirror pairSe67andAs67

Recent experimental data have revealed large mirror energy differences (MED) between high-spin states in the mirror nuclei $^{67}\mathrm{Se}$ and $^{67}\mathrm{As}$, the heaviest pair where MED have been determined so far. The MED are generally attributed to the isospin symmetry breaking caused by the Coulomb force and by the isospin-nonconserving part of the nucleon-nucleon residual interaction. The different contributions of the various terms have been extensively studied in the $\mathit{fp}$ shell. By employing large-scale shell-model calculations, we show that the inclusion of the ${g}_{9/2}$ orbit causes interference between the electromagnetic spin-orbit and the Coulomb monopole radial terms at high spin. The large MED are attributed to the aligned proton pair excitations from the ${p}_{3/2}$ and ${f}_{5/2}$ orbits to the ${g}_{9/2}$ orbit. The relation of the MED to deformation is discussed.

FIRST γ-RAY SPECTROSCOPY AND ISOSPIN SYMMETRY STUDY OF THE N = Z - 2 NUCLEUS 44V

Excited states in the Tz = -1 nucleus 44 V have been observed for the first time. The states have been identified through recoil-γ-γ coincidences and comparison with analogue states in the mirror nucleus 44 Sc . Mirror energy differences have been extracted and compared to state-of-the-art fp shell-model calculations which include charge symmetry breaking forces.

Firstγ-ray spectroscopy ofFe49andNi53: Isospin-breaking effects at large proton excess

Isospin-breaking effects have been studied for the first time in $T=\frac{3}{2}$ isobaric analog states. Gamma decays have been observed from ${T}_{z}=\ensuremath{-}\frac{3}{2}$ nuclei, $^{49}\mathrm{Fe}$ and $^{53}\mathrm{Ni}$, presented here in new level schemes, and mirror energy differences have been computed following observation of analog states in $^{49}\mathrm{V}$ and $^{53}\mathrm{Mn}$, respectively. Shell-model calculations in the $\mathit{fp}$ shell are in good agreement with the data and reveal the importance of non-Coulomb isospin-breaking effects in $T=\frac{3}{2}$ isobaric analog states. A two-step fragmentation process was developed to allow access to highly proton-rich nuclei and to produce each member of a mirror pair via mirrored fragmentation of a $^{56}\mathrm{Ni}$ secondary beam. This work represents the first study using this technique and demonstrates the power of this approach for future studies of isobaric analog states in very proton-rich systems.

Mirror energy differences and nuclear structure in 1f7/2 nuclei

Experimental mirror energy differences (MED) for nuclei lying in the middle and the second part of the 1f 7/2 shell are compared with shell model calculations in the 1f 7/2 and in the full pf configuration spaces, as well as with cranked shell model calculations. MED plots are fully consistent with the description which emerges from the interpretation of SM calculations: i.e. the band-crossing of the gs band with high-K bands in A = 51 and 50 mirror pairs, as well as the seniority-3 quasi band-termination at \(\ensuremath I^{\pi} = 19/2^-\) in A = 49 . Rotational alignment effects are excluded, contrarily to what even recently proposed. Some inconsistencies, as well as definition improprieties, are pointed out in the topical literature.

Isospin asymmetry effects in mirror nuclei with modern charge-dependent NN potential

The properties of T = 1 / 2 mirror nuclei in the lower fp shell have been investigated with a microscopic isospin-nonconserving effective Hamiltonian. The two-body interaction of the Hamiltonian is derived from a high-precision charge-dependent Bonn nucleon–nucleon potential using the G-matrix folded-diagram renormalization method. The level schemes and transition properties of the nuclei are calculated, obtaining reasonable agreements with existing experimental data and other theoretical calculations. The charge-dependent effective Hamiltonian provides a microscopic basis for the study of the isospin-symmetry-breaking effect in many-body nuclear systems. The effect is discussed with different methods and compared with experimental observations by calculating the mirror energy difference (MED) which is a sensitive probe to measure the effect.

Spectroscopy ofMg20: The isobaric mass multiplet equation for the2+states of theA=20,T=2quintet and distant mirror nuclei

We report on the first determination of the ${2}_{1}^{+}$ energy of $^{20}\mathrm{Mg}$, the most neutron-deficient Mg isotope known to exist. The result, $E({2}_{1}^{+})=1598(10)$ keV, obtained from in-beam \ensuremath{\gamma}-ray spectroscopy following the two-neutron removal from a $^{22}\mathrm{Mg}$ secondary beam, is discussed in the framework of the isobaric mass multiplet equation (IMME). Resulting predictions for the excitation energies of the $T=2,{2}^{+}$ states in the $^{20}\mathrm{F}$ and $^{20}\mathrm{Na}$ isobars are presented. The mirror energy difference, $E({2}_{1}^{+},$$^{20}\mathrm{Mg}$$)\ensuremath{-}E({2}_{1}^{+},$$^{20}\mathrm{O}$$)=\ensuremath{-}77(10)$ keV, is compared to a recent prediction within the nuclear shell model based on the ``${\mathrm{USD}}^{m}$ - gap Z14'' modification of the universal $\mathit{sd}$ (USD) effective interaction.

The T=2 mirrors 36Ca and 36S: A test for isospin symmetry of shell gaps at the driplines

Abstract The first excited 2 + state of 36Ca has been identified by its γ-decay, exploiting the two-step fragmentation technique at the FRS-RISING setup at GSI. This is the heaviest T z = − 2 nucleus in the Segre chart in which a γ-decay of an excited state has been observed. A stable beam of 40Ca at 420 A MeV impinged on a primary 9Be target. Out of the secondary beam of fragmentation products, 37Ca was separated by the FRS and struck on a second 9Be target at the final focus of the FRS. The energy for the 2 1 + decay of 36Ca was determined to be 3015(16) keV, which is 276 keV lower than in its T = 2 mirror 36S. This mirror energy difference (MED) is discussed in the framework of shell model calculations using a 16O core, the sd shell isospin symmetric interaction USD and experimental single-particle energies from 17O and 17F. The results show that the MED within the sd shell provide a sensitive test for the evolution of the N, Z = 14 , 16 subshell gaps towards the driplines. Especially the N, Z = 16 gap is determined by Thomas–Ehrman shift in the A = 17 , T = 1 / 2 isospin doublet, while Coulomb effects are found to have marginal influence.

Spectroscopy of theN=Z−2nucleusCr46and mirror energy differences

Excited states in $^{46}\mathrm{Cr}$ were sought using the $^{12}\mathrm{C}$($^{36}\mathrm{Ar}$,$2n$) reaction. Gamma rays were detected with the Gammasphere array, and the $Z$ value of the reaction products was determined with an ionization chamber located at the focal plane of the Fragment Mass Analyzer. In addition to the ground-state band observed up to ${I}^{\ensuremath{\pi}}={10}^{+}$ (tentatively ${12}^{+}$), five states are proposed to belong to the ${3}^{\ensuremath{-}}$ band. The mirror energy differences with the analog states in $^{46}\mathrm{Ti}$ present a pronounced staggering effect between the odd and even spin members that is reproduced well by shell-model calculations incorporating the different Coulomb contributions, monopole, multipole, and single-particle effects together with an isospin-nonconserving interaction that accounts for the so-called $J=2$ anomaly. Dramatically different $E1$ decay patterns for members of the ${3}^{\ensuremath{-}}$ band between the $^{46}\mathrm{Cr}$ and $^{46}\mathrm{Ti}$ mirrors are also observed.

Spectroscopy of the N=Z-2 nucleus Cr46 and mirror energy differences

Spectroscopy of the N=Z-2 nucleus Cr46 and mirror energy differences

Observation ofNi54: Cross-Conjugate Symmetry inf7/2Mirror Energy Differences

Gamma decays from excited states up to Jpi=6+ in the N=Z-2 nucleus 54Ni have been identified for the first time. Level energies are compared with those of the isobars 54Co and 54Fe and of the cross-conjugate nuclei of mass A=42. The good but puzzling f7/ cross-conjugate symmetry in mirror and triplet energy differences is analyzed. Shell model calculations reproduce the new data but the necessary nuclear charge-dependent phenomenology is not fully explained by modern nucleon-nucleon potentials.

Coulomb energy differences in mirror nuclei

By comparing the excitation energies of analogue states in mirror nuclei, several nuclear structure properties can be studied as a function of the angular momentum up to high spin states. They can be described in the shell model framework by including electromagnetic and nuclear isospin-non-conserving interactions. Calculations for the mirror energy differences in nuclei of the f7/2shell are described and compared with recent experimental data. These studies are extended to mirror nuclei in the upper sd and fp shells.

MIRROR SYMMETRY IN THE UPPER fp SHELL

A detailed investigation of the contribution from Coulomb effects to the observed mirror energy difference diagrams in nuclei in the lower part of the upper fp shell is presented by means of large-scale shell-model calculations.

Mirror energy differences in theA=31mirror nuclei,S31andP31, and their significance in electromagnetic spin-orbit splitting

Excited states in $^{31}\mathrm{S}$ and $^{31}\mathrm{P}$ were populated in the $^{12}\mathrm{C}$($^{20}\mathrm{Ne}$,n) and $^{12}\mathrm{C}$($^{20}\mathrm{Ne}$,p) reactions, respectively, at a beam energy of 32 MeV. High spin states of positive and negative parity have been observed in $^{31}\mathrm{S}$ for the first time, and the yrast scheme of $^{31}\mathrm{P}$ has been extended. Large mirror energy differences between the first $9/{2}^{\ensuremath{-}}$ and $13/{2}^{\ensuremath{-}}$ states were observed, but only small differences for the first $7/{2}^{\ensuremath{-}}$ and $11/{2}^{\ensuremath{-}}$ levels. The significance of these observations is discussed in relation to the electromagnetic spin-orbit effect and the relative binding energy of the levels.

News on mirror nuclei in the sd and fp shells

Novel experimental results on mirror nuclei in the sd and fp shells are presented. Their respective Mirror Energy Difference (MED) diagrams are interpreted by means of large-scale shell-model calculations. A unique way of extracting effective charges from isospin symmetry studies is also discussed.

Mirror energy differences in the A=31 mirror nuclei, S31 and P31, and their significance in electromagnetic spin-orbit splitting

Mirror energy differences in the A=31 mirror nuclei, S31 and P31, and their significance in electromagnetic spin-orbit splitting