Isospin Purity Research Articles

Semi-empirical evaluation of isospin mixing from forbidden E1 transitions

ΔT = 0 electric dipole transitions in self conjugate nuclei, forbidden by isospin selection rules, are readily seen in nature. This implies that the states participating in these transitions may not be of pure isospin T. This work identifies some of these transitions in a few upper-sd shell self-conjugate nuclei and attempts to calculate the degree of isospin mixing in these nuclei by using the standard two-level mixing formalism in a semi-empirical approach. The physically observed E1 transitions are broken down into two theoretically allowed ΔT = 1 channels. These allowed components have been calculated within the shell model. Our results are consistent with both theoretical and experimental values found in the literature.

Theoretical study of the Ω(2012) state in the Ωc0→π+Ω(2012)−→π+(K¯Ξ)− and π+(K¯Ξπ)− decays

We report on a theoretical study of the newly observed $\Omega(2012)$ resonance in the nonleptonic weak decays of $\Omega_c^0 \to \pi^+ \bar{K}\Xi^*(1530) (\eta \Omega) \to \pi^+ (\bar{K}\Xi)^-$ and $\pi^+ (\bar{K}\Xi\pi)^-$ via final-state interactions of the $\bar{K}\Xi^*(1530)$ and $\eta \Omega$ pairs. The weak interaction part is assumed to be dominated by the charm quark decay process: $c(ss) \to (s + u + \bar{d})(ss)$, while the hadronization part takes place between the $sss$ cluster from the weak decay and a quark-antiquark pair with the quantum numbers $J^{PC} = 0^{++}$ of the vacuum, produces a pair of $\bar{K}\Xi^*(1530)$ and $\eta \Omega$. Accordingly, the final $\bar{K}\Xi^*(1530)$ and $\eta \Omega$ states are in pure isospin $I= 0$ combinations, and the $\Omega_c^0 \to \pi^+ \bar{K}\Xi^*(1530)(\eta \Omega) \to \pi^+ (\bar{K}\Xi)^-$ decay is an ideal process to study the $\Omega(2012)$ resonance. With the final-state interaction described in the chiral unitary approach, up to an arbitrary normalization, the invariant mass distributions of the final state are calculated, assuming that the $\Omega(2012)$ resonance with spin-parity $J^P = 3/2^-$ is a dynamically generated state from the coupled channels interactions of the $\bar{K}\Xi^*(1530)$ and $\eta \Omega$ in $s$-wave and $\bar{K}\Xi$ in $d$-wave. We also calculate the ratio, $R^{\bar{K}\Xi\pi}_{\bar{K}\Xi} = {\rm Br}[\Omega_c^0 \to \pi^+ \Omega(2012)^- \to \pi^+ (\bar{K}\Xi \pi)^-] / {\rm Br}[\Omega_c^0 \to \pi^+ \Omega(2012)^- \to \pi^+ (\bar{K}\Xi)^-$]. The proposed mechanism can provide valuable information on the nature of the $\Omega(2012)$ and can in principle be tested by future experiments.

Isospin dependence of electromagnetic transition strengths among an isobaric triplet

Electric quadrupole matrix elements, Mp, for the Jπ=2+→0+, ΔT=0, T=1 transitions across the A=46 isobaric multiplet 46Cr-46V-46Ti have been measured at GSI with the FRS-LYCCA-AGATA setup. This allows direct insight into the isospin purity of the states of interest by testing the linearity of Mp with respect to Tz. Pairs of nuclei in the T=1 triplet were studied using identical reaction mechanisms in order to control systematic errors. The Mp values were obtained with two different methodologies: (i) a relativistic Coulomb excitation experiment was performed for 46Cr and 46Ti; (ii) a “stretched target” technique was adopted here, for the first time, for lifetime measurements in 46V and 46Ti. A constant value of Mp across the triplet has been observed. Shell-model calculations performed within the fp shell fail to reproduce this unexpected trend, pointing towards the need of a wider valence space. This result is confirmed by the good agreement with experimental data achieved with an interaction which allows excitations from the underlying sd shell. A test of the linearity rule for all published data on complete T=1 isospin triplets is presented.

Σ1/2−*(1380) in the Λc+→ηπ+Λ decay

A $\Sigma^*$ state with spin-parity $J^P = 1/2^-$ with mass and width around $1380$ MeV and $120$ MeV, refereed to as the $\Sigma^*_{1/2^-}(1380)$, has been predicted in several pentaquark models and inferred from the analysis of CLAS $\gamma p$ data. In the present work, we discuss how one can employ the $\Lambda^+_c \to \eta \pi^+ \Lambda$ decay to test its existence, as well as to study the $\Sigma^*(1385)$ state with $J^P = 3/2^+$. Because the final $\pi^+ \Lambda$ system is in a pure isospin $I = 1$ combination, the $\Lambda^+_c \to \eta \pi^+ \Lambda$ decay can be an ideal process to study these $\Sigma^*$ resonances. In particular, we show that the decay angle and energy distributions of the $\pi^+$ are very different for $\Sigma^*(1385)$ and $\Sigma^*_{1/2^-}(1380)$. The proposed decay mechanism as well as the existence of the $\Sigma^*_{1/2^-}(1380)$ state can be checked by future BESIII and Belle experiments.

Constraints on the S=-1 meson-baryon interaction at NLO

This work contains a study of the meson-baryon interaction in the S = −1 sector by means of a chiral SU (3) Lagrangian up to next-to-leading order (NLO) and implementing unitarization in coupled channels. In order to get more reliable values of the parameters which are present in the model, we performed several fits which take a large set of experimental scattering data in different two-body channels, threshold branching ratios, and the precise SIDDHARTA values of the energy shift and width of kaonic hidrogen into consideration. In previous studies, we had shown that the K − p → K Ξ reactions are especially sensitive to the next to Weinberg-Tomozawa (WT) corrections in the hierarchy. In addition, we pointed out the need to employ processes which are described by pure isospin amplitudes as a tool to discern which models are more realistic among those which give small values for the χ 2 in the fits. Following the former suggestion, we present results which include data from K − p → η Λ, η Σ reactions which have pure isospin I = 0 and I = 1 component respectively. Finally, to check the goodness of the new obtained parametrization of the model, we present a prediction for another process that filters the I = 1 isospin component: the pure I = 1 reaction which could be measured at the proposed secondary K 0 L beam at Jlab.

The $$a_0(980)$$ a 0 ( 980 ) and $$\Lambda (1670)$$ Λ ( 1670 ) in the $$\Lambda ^+_c \rightarrow \pi ^+ \eta \Lambda $$ Λ c + → π + η Λ decay

We propose to study the $a_0(980)$ and the $\Lambda(1670)$ resonances in the $\Lambda^+_c \to \pi^+ \eta \Lambda$ decay via the final state interactions of the $\pi^+ \eta$ and $\eta \Lambda$ pairs. The weak interaction part proceeds through the $c$ quark decay process: $c(ud) \to (s + u + \bar d)(ud)$, while the hadronization part takes place in two different mechanisms. In the first mechanism, the $sud$ cluster picks up a $q\bar{q}$ pair from the vacuum to form the $\eta\Lambda$ meson-baryon pair while the $u\bar{d}$ pair from the weak decay hadronizes into a $\pi^+$. In the second, the $sud$ cluster turns into a $\Lambda$, while the $u\bar{d}$ pair from the $c$ decay picks up a $q\bar{q}$ pair and hadronizes into a meson-meson pair ($\pi\eta$ or $K\bar{K}$). Because the final $\pi^+ \eta$ and $\eta \Lambda$ states are in pure isospin $I = 1$ and $I=0$ combinations, the $\Lambda^+_c \to \pi^+ \eta \Lambda$ decay can be an ideal process to study the $a_0(980)$ and $\Lambda(1670)$ resonances. Describing the final state interaction in the chiral unitary approach, we find that the $\pi^+ \eta$ and $\eta \Lambda$ invariant mass distributions, up to an arbitrary normalization, show clear cusp and peak structures, which can be associated with the $a_0(980)$ and $\Lambda(1670)$ resonances, respectively. The proposed mechanism can provide valuable information on the nature of these resonances and can in principle be test by facilities such as BEPCII.

Possible Existence of Light Hypernuclei

The possible existence of light Σ hypernuclei is discussed together with their general binding mechanism. The coupling between the isotriplet Σ particle (Σ+, Σ0 and Σ−) and the corresponding nuclear core isomultiplet and supermultiplet which comes from the strong isospin dependent and isospin-spin dependent terms of Σ-N interaction plays a crucial role to produce bound states of light Σ hypernuclei. It is found that 1) an almost pure isospin 1/2 bound (ground) state appears in Σ4He mainly due to the cooperative contribution of the (tN·tΣ) and (tN·tΣ)(sN·sΣ) terms of Σ-N interaction, and 2) an isospin-breaking bound (ground) state appears in Σ7Li mainly due to the (tN·tΣ)(sN·sΣ) term of Σ-N interaction. We discuss in detail the different binding mechanism between Σ4He and Σ7Li and propose a threshold rule for the formation of bound Σ hypernuclear states. From the viewpoint of the threshold rule, the possible existence of other typical light Σ hypernuclei, Σ7H, Σ9Be and Σ11B, are investigated together with their binding mechanism on the same footing as Σ4He and Σ7Li.

Isospin purity ofT=1states in theA=38nuclei studied via lifetime measurements inK38

The Doppler Shift Attenuation Method was used to measure lifetimes for levels in $^{38}\mathrm{K}$ at excitation energies of 1698, 2404, 2830, 2996, and 3671 keV, populated using the $^{40}\mathrm{Ca}$(d, \ensuremath{\alpha})$^{38}\mathrm{K}$ reaction at a beam energy of 4.5 MeV. Values of 109(29), 95(22), 457(63), 130(40), and 160(50) fs, respectively, were measured and are compared with previous values obtained using different stopping powers. The matrix element for the transition between the ${J}^{\ensuremath{\pi}}={2}_{T=1}^{+}$ and ${0}_{T=1}^{+}$ states in this ${T}_{z}=0$ nucleus is compared with the analogous transition in the other nuclei in the $T=1$ triplet, $^{38}\mathrm{Ca}$ (${T}_{z}=\ensuremath{-}1$) and $^{38}\mathrm{Ar}$ (${T}_{z}=+1$), and with the results of shell-model calculations.

N* PRODUCTION FROM J/ψ DECAYS AT BES

The πN system in [Formula: see text] is limited to be pure isospin 1/2 due to isospin conservation. This is a big advantage in studying N*→πN from the J/ψ decays, compared with πN and γN experiments which mix isospin 1/2 and 3/2 for πN system. Based on the 58 million J/ψ data collected at the Beijing Electron Positron Collider, [Formula: see text] and other decay channels are analyzed. In the decay [Formula: see text], three peaks show up very clearly at 1400 MeV/c2, 1500 MeV/c2 and 1670 MeV/c2 in the πN invariant mass spectrum with additional peak around 2030 MeV/c2 which may be caused by a new N* resonance.

Test of isospin purity in theA=42isobaric analogs

A careful measurement of the lifetime of the first ${2}_{T=1}^{+}$ state in $^{42}\mathrm{Sc}$ has allowed an accurate experimental test of isospin purity in the $A=42$ isobaric analogs by using the isospin formalism. A lifetime of $69\phantom{\rule{0.3em}{0ex}}(18)\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ has been determined, giving an isoscalar matrix element of $6.8\phantom{\rule{0.3em}{0ex}}(8)\phantom{\rule{0.3em}{0ex}}\mathrm{W.u.}$ Previous measurements of the lifetimes in the mirror nuclei $^{42}\mathrm{Ca}$ and $^{42}\mathrm{Ti}$ provided an isoscalar matrix element of $7.1\phantom{\rule{0.3em}{0ex}}(5)\phantom{\rule{0.3em}{0ex}}\mathrm{W.u.}$ which is very close to the presently measured value for $^{42}\mathrm{Sc}$.

Giant dipole radiation and isospin purity in highly excitedS nuclei

Giant dipole radiation and isospin purity in highly excitedS nuclei

Giant dipole radiation and isospin purity in highly excitedS nuclei

We have extracted the degree of isospin mixing in 32 S at the excitation energy of 58 MeV by comparing measured and calculated high-energy γ-ray spectra from the statistical decay of the 32 S and 31 P compound nuclei formed in heavy-ion fusion reactions. We have found that the isospin mixing is small in agreement with theoretical predictions.

Giant dipole radiation and isospin purity in highly excited 32S nuclei

We have extracted the degree of isospin mixing in 32S at the excitation energy of 58 MeV by comparing measured and calculated high-energy γ-ray spectra from the statistical decay of the 32S and 31P compound nuclei formed in heavy-ion fusion reactions. We have found that the isospin mixing is small in agreement with theoretical predictions.

Neutron skin and isospin structure of giant resonances

Neutron number dependence of neutron skin thickness in several isotopes is discussed by using Skyrme Hartree-Fock (HF) calculations. It is shown that the size of neutron skin is proportional to one-third power of the neutron number in all the isotopes studied although the central density varies substantially in each isotope. The isospin structure of giant quadrupole resonances (GQR) is also studied using self-consistent HF + random phase approximations. The isovector GQR is found to be a good isospin mode even in very neutron-rich nuclei, while the isoscalar GQR shows a large deviation from the pure isospin mode in neutron-rich C and O isotopes due to a strong neutron skin effect.

Main channels of the decay of the giant dipole resonance in the 20,22Ne nuclei and isospin splitting of the giant dipole resonance in the 22Ne nucleus

Data published in the literature on various photonuclear reactions for the 20,22Ne isotopes and for their natural mixture are analyzed with the aim of exploring special features of the decay of giant-dipole-resonance states in these two isotopes. With the aid of data on the abundances of the isotopes and on the energy reaction thresholds, the cross sections for the reactions 20,22Ne[(γ, n)+(γ, np)] and 20,22Ne[(γ, p)+(γ, np)] are broken down into the contributions from the one-nucleon reactions (γ, n) and (γ, p) and the contributions from the reactions (γ, np). The cross sections for the reactions 20,22Ne(γ, n)19,21Ne and 20,22Ne(γ, p)19,21F in the energy range Eγ=16.0–28.0 MeV and the cross sections for the reactions 20,22Ne(γ, np)18,20F in the energy range Eγ=23.3–28.0 MeV are estimated. The behavior of the cross-section ratio r=σ(γ, p)/σ(γ, n) for the 22Ne nucleus as a function of energy is analyzed, and the isospin components of the giant dipole resonance in the 22Ne nucleus are identified. The contributions of the isospin components of the giant dipole resonance in the 22Ne nucleus to the cross sections for various photonuclear reactions are determined on the basis of an analysis of the diagram of the excitation and decay of pure isospin states in the 22Ne nucleus and in nuclei neighboring it, which are members of the corresponding isospin multiplets. The isospin splitting of the giant dipole resonance and the ratio of the intensities of the isospin components are determined to be ΔE=4.57±0.69 MeV and R=0.24±0.04, respectively.

Study of N*(1440) from J/Ψ decays

For $J/\Psi\to\bar pp \pi^0$ and $\bar pp\pi^+\pi^-$, the $\pi^0p$ and $p\pi^+\pi^-$ systems are limited to be pure isospin 1/2 due to isospin conservation. This is a big advantage in studying $N^*$ resonances from $J/\Psi$ decays, compared with $\pi N$ and $\gamma N$ experiments. The process $J/\Psi\to\bar pN^*$ or $p\bar N^*$ provides a new way to probe the internal structure of the $N^*$ resonances. Here we report a quark model calculation for $J/\Psi\to\bar pp$, $pN^*(1440)$ and $\bar N^*N^*$. The implication for the internal structure of $N^*(1440)$ is discussed.

B(E2;0g.s.+→21+)in18Neand isospin purity inA=18nuclei

The ${0}_{\mathrm{g}.\mathrm{s}.}^{+}\ensuremath{\rightarrow}{2}_{1}^{+}$ excitation in the proton-rich nucleus ${}^{18}\mathrm{Ne}$ has been studied via intermediate energy heavy-ion scattering with a beam of this radioactive isotope. The observed $\ensuremath{\gamma}$-ray yields have been combined with coupled channels calculations of the inelastic scattering reactions to obtain the electromagnetic matrix element ${B(E2;0}_{\mathrm{g}.\mathrm{s}.}^{+}\ensuremath{\rightarrow}{2}_{1}^{+}).$ This result is combined with the corresponding results in the mirror nucleus ${}^{18}\mathrm{O}$ and the $T=1$ states in the $N=Z$ nucleus ${}^{18}\mathrm{F}$ as a test of isospin purity.

The baryon spectroscopy from [formula omitted] decays

J ψ decay at Beijing Electron-Positron Collider (BEPC) is well known as the best place for looking for glueballs. But in fact it is also an excellent place for studying N ∗ and hyperon physics. For J ψ → N Nππ , and N Nππ the πN and ππN systems are limited to be pure isospin 1 2 due to isospin conservation. This is a big advantage in studying N ∗ resonances from J ψ decays, compared with the πN and γN experiments which suffer difficulty on the isospin decomposition of 1 2 and 3 2 . There are also plenty other decay modes of J ψ involving baryon-antibaryon pairs plus mesons which can be used to study N ∗ and hyperon resonances, e.g., looking for the “missing” N ∗ states from J ψ → ppω , ppη′ , pK − Λ , etc.; studying N ∗(1535) → ηp from J ψ → ppη and studying Λ(1405) → Σπ from J ψ → Λ Σ −π + . It provides a new way to study the internal structure of baryon resonances. The newest progress and outlook in this field are presented.

Coulomb corrections to low energy antiproton annihilation cross sections on protons and nuclei

We calculate, in a systematic way, the enhancement effect on $\overline{p}p$ and $\overline{p}A$ annihilation cross sections at low energy due to the initial state electrostatic interaction between the projectile and the target nucleus. This calculation is aimed at future comparisons between $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}$ and $\overline{p}$ annihilation rates on different targets for the extraction of pure isospin channels.

Chaotic dynamics and collective modes

General properties of nuclear collective excitations interacting with a chaotic background are discussed, both in the discrete spectrum and in the continuum. Strength functions and spreading widths at weak and strong damping are considered and related to the observable reaction cross sections. Theory predicts saturation of the spreading width, restoration of isospin purity and disappearance of the collective strength at high excitation energy.