Intermediate Nuclear States Research Articles

Induced Isotensor Interactions in Heavy-Ion Double-Charge-Exchange Reactions and the Role of Initial and Final State Interactions

The role of initial state (ISI) and final state (FSI) ion–ion interactions in heavy-ion double-charge-exchange (DCE) reactions A(Z,N)→A(Z±2,N∓2) are studied for double single-charge-exchange (DSCE) reactions given by sequential actions of the isovector nucleon–nucleon (NN) T-matrix. In momentum representation, the second-order DSCE reaction amplitude is shown to be given in factorized form by projectile and target nuclear matrix elements and a reaction kernel containing ISI and FSI. Expanding the intermediate propagator in a Taylor series with respect to auxiliary energy allows us to perform the summation in the leading-order term over intermediate nuclear states in closure approximation. The nuclear matrix element attains a form given by the products of two-body interactions directly exciting the n2p−2 and p2n−2 DCE transitions in the projectile and the target nucleus, respectively. A surprising result is that the intermediate propagation induces correlations between the transition vertices, showing that DSCE reactions are a two-nucleon process that resembles a system of interacting spin–isospin dipoles. Transformation of the DSCE NN T-matrix interactions from the reaction theoretical t-channel form to the s-channel operator structure required for spectroscopic purposes is elaborated in detail, showing that, in general, a rich spectrum of spin scalar, spin vector and higher-rank spin tensor multipole transitions will contribute to a DSCE reaction. Similarities (and differences) to two-neutrino double-beta decay (DBD) are discussed. ISI/FSI distortion and absorption effects are illustrated in black sphere approximation and in an illustrative application to data.

Excitation and probing of low-energy nuclear states at high-energy storage rings

$^{229}\mathrm{Th}$ with a low-lying nuclear isomeric state is an essential candidate for a nuclear clock as well as many other applications. Laser excitation of the isomeric state has been a long-standing goal. With relativistic $^{229}\mathrm{Th}$ ions in storage rings, high-power lasers with wavelengths in the visible range or longer can be used to achieve high excitation rates of $^{229}\mathrm{Th}$ isomers. This can be realized through direct resonant excitation or excitation via an intermediate nuclear or electronic state, facilitated by the tunability of both the laser-beam and ion-bunch parameters. Unique opportunities are offered by highly charged $^{229}\mathrm{Th}$ ions due to the nuclear-state mixing. The significantly reduced isomeric-state lifetime corresponds to a much higher excitation rate for direct resonant excitation. Importantly, we propose electric dipole transitions changing both the electronic and nuclear states that are opened by the nuclear hyperfine mixing. We suggest using them for efficient isomer excitation in Li-like $^{229}\mathrm{Th}$ ions, via stimulated Raman adiabatic passage or single-laser excitation. We also propose schemes for probing the isomers, utilizing nuclear radiative decay or laser spectroscopy on electronic transitions, through which the isomeric-state energy can be determined with an orders-of-magnitude higher precision than the current value. The schemes proposed here for $^{229}\mathrm{Th}$ could also be adapted to low-energy nuclear states in other nuclei, such as $^{229}\mathrm{Pa}$.

Perfect adaptation achieved by transport limitations governs the inorganic phosphate response in S. cerevisiae

Cells cope with and adapt to ever-changing environmental conditions. Sophisticated regulatory networks allow cells to adjust to these fluctuating environments. One such archetypal system is the Saccharomyces cerevisiae Pho regulon. When external inorganic phosphate (Pi) concentration is low, the Pho regulon activates, expressing genes that scavenge external and internal Pi. However, the precise mechanism controlling this regulon remains elusive. We conducted a systems analysis of the Pho regulon on the single-cell level under well-controlled environmental conditions. This analysis identified a robust, perfectly adapted Pho regulon state in intermediate Pi conditions, and we identified an intermediate nuclear localization state of the transcriptional master regulator Pho4p. The existence of an intermediate nuclear Pho4p state unifies and resolves outstanding incongruities associated with the Pho regulon, explains the observed programmatic states of the Pho regulon, and improves our general understanding of how nature evolves and controls sophisticated gene regulatory networks. We further propose that robustness and perfect adaptation are not achieved through complex network-centric control but by simple transport biophysics. The ubiquity of multitransporter systems suggests that similar mechanisms could govern the function of other regulatory networks as well.

Imaging and sensing of pH and chemical state with nuclear-spin-correlated cascade gamma rays via radioactive tracer

Single-photon-emission computed tomography (SPECT) and positron-emission tomography (PET) are highly sensitive molecular detection and imaging techniques that generally measure accumulation of radio-labeled molecules by detecting gamma rays. Quantum sensing of local molecular environment via spin, such as nitrogen vacancy (NV) centers, has also been reported. Here, we describe quantum sensing and imaging using nuclear-spin time-space correlated cascade gamma-rays via a radioactive tracer. Indium-111 (111In) is widely used in SPECT to detect accumulation using a single gamma-ray photon. The time-space distribution of two successive cascade gamma-rays emitted from an 111In atom carries significant information on the chemical and physical state surrounding molecules with double photon coincidence detection. We propose and demonstrate quantum sensing capability of local micro-environment (pH and chelating molecule) in solution along with radioactive tracer accumulation imaging, by using multiple gamma-rays time-and-energy detection. Local molecular environment is extracted through electric quadrupole hyperfine interaction in the intermediate nuclear spin state by the explicit distribution of sub-MeV gamma rays. This work demonstrates a proof of concept, and further work is necessary to increase the sensitivity of the technique for in vivo imaging and to study the effect of scattered radiation for possible application in nuclear medicine.

Surface direct nuclear photoeffect in heavy deformed nuclei

A mechanism of photon-induced direct knockout of a nucleon from the nuclear surface without formation of intermediate excited nuclear state is described. The effect plays an important role at least for the $(\ensuremath{\gamma},p)$ reaction on heavy nuclei in the energy region centered at about 30 MeV where the probability of formation of the giant dipole resonance is already small but quasideuteron photoabsorption still does not prevail. A compact model of the surface direct nuclear photoeffect (SDNP) in heavy deformed nuclei that can be used to calculate the differential $d\ensuremath{\sigma}({E}_{\ensuremath{\gamma}},\ensuremath{\vartheta})/d\mathrm{\ensuremath{\Omega}}$ and total $\ensuremath{\sigma}({E}_{\ensuremath{\gamma}})$ cross sections of the SDNP under adiabatic approximation is formulated. The model is applied to calculation of the $(\ensuremath{\gamma},p)$ reaction cross sections on $^{160}\mathrm{Gd}$ and $^{184,186}\mathrm{W}$. The importance of the SDNP effect for these nuclei at ${E}_{\ensuremath{\gamma}}\ensuremath{\sim}30$ MeV is demonstrated.

Overlap of quasiparticle random-phase approximation states based on ground states of different nuclei: Mathematical properties and test calculations

The overlap of the excited states in quasiparticle random-phase approximation (QRPA) is calculated to simulate the overlap of the intermediate nuclear states of the double-$\ensuremath{\beta}$ decay. Our basic idea is to use the like-particle QRPA with the aid of the closure approximation and calculate the overlap as rigorously as possible by making use of the explicit equation of the QRPA ground state. The formulation is shown in detail, and the mathematical properties of the overlap matrix are investigated. Two test calculations are performed for relatively light nuclei with the Skyrme and volume $\ensuremath{\delta}$-pairing energy functionals. The validity of the truncations used in the calculation is examined and confirmed.

Overlap of quasiparticle random-phase approximation states for nuclear matrix elements of the neutrino-less double-βdecay

Quasiparticle random-phase approximation (QRPA) is applied to two nuclei, and the overlap of the QRPA excited states based on the different nuclei is calculated. The aim is to calculate the overlap of intermediate nuclear states of the double-$\ensuremath{\beta}$ decay. We use the like-particle QRPA after the closure approximation is applied to the nuclear matrix elements. The overlap is calculated rigorously by making use of the explicit equation of the QRPA ground state. The formulation of the overlap is shown, and a test calculation is performed. The effectiveness of the truncations used is shown.

Photoexcitation of the quasi-bound isobar nuclear state of a nucleus in the (γ,πN) reaction

The data from three experiments performed on the Saclay linac, at the Tomsk synchrotron, and at the MAMI accelerator in Maintz, in which single pion photoproduction on light nuclei was accompanied by the emission of nucleons, are analyzed. The behavior of the experimental cross sections, which cannot be explained in the impulse approximation, is interpreted in a model where an intermediate quasi-bound isobar nuclear state is formed and decays with the emission of a pion and a nucleon.

Recent results on [formula omitted] absorption at rest by few nucleons and the bound kaonic nuclear state puzzle

Data from the K stop − A absorption reaction in light nuclei ( 6,7Li, 9Be, 13C and 16O) have recently been collected by FINUDA at DAΦNE, INFN Laboratori Nazionali di Frascati (LNF), Italy. The studies of kaon absorption on multibaryonic systems have been carried out by examining Λ p ( d , t ) correlations. The observation of a nearly constant rate of Λ p ( d , t ) pairs emitted in opposite direction for the targets examined suggests that the absorption of K − at rest in nuclei proceeds through the formation of an intermediate nuclear state, often named Bound Kaonic Nuclear (BKN) state. The experimental study of such states is based on the behavior of the Λ p ( d , t ) invariant masses, which allow the structure of bound [ K − NN( NNN, NNNN)] systems in nuclei to be examined. Missing mass distributions supply complementary information on the dynamics of the K − absorption.

On the mechanism of the photoproduction of pion-nucleon pairs on nuclei

The data from an experiment performed at the MAMI accelerator in Maintz in which the differential cross sections for the photoproduction of positive pions on the carbon nucleus accompanied by the emission of nucleons have been analyzed. The behavior of the experimental cross sections as functions of the pion energy and nucleon emission angle, which cannot be explained in the quasi-free approximation, is interpreted in a model where an intermediate quasi-bound isobar nuclear state is formed and decays with the emission of a pion and a nucleon.

A treatment of medium-energy particle induced fission for spallation-systems’ calculations

A method for including medium-energy fission into neutronic calculations for spallation systems is described and discussed. The basis is a semi-empirical evaporation plus fission model able to treat a wide range of nuclear states in the mass region above about 100amu with nuclear excitation energies up to 1000MeV. In combination with suitable nuclear physics models describing the entrance channels and a suitable evaporation algorithm, this is able to give a full description of the de-excitation of the intermediate nuclear states formed in interactions with target nuclei from Ag to Cf by (i) medium energy (up to a few GeV) nucleons and pions, (ii) thermal and fast neutrons and (iii) light ions with energy up to several 100MeV/A.

Neutrino accompanied [formula omitted], [formula omitted] and [formula omitted] processes within single state dominance hypothesis

The systematic study of (anti)neutrino accompanied β ± β ± decays and β + / EC , EC / EC electron capture is performed under the assumption of single intermediate nuclear state dominance. The corresponding half-lives are evaluated both for transitions to the ground state as well as to the 0 + and 2 + excited states of final nucleus. It is stressed that the hypothesis of single state dominance can be confirmed or ruled out by the precision measurements of the differential characteristics of the 2 ν β − β − -decays of 100Mo and 116Cd as well as β + / EC electron capture in 106Cd, 130Ba and 136Ce.

Probing double beta decay by nuclear muon capture

A reliable theoretical calculations on two-neutrino and neutrinoless double-beta-decay rates requires a solid description about the nuclear structure of the intermediate nuclear states. It has been suggested that the ordinary muon capture could be used to probe the structure of the intermediate states in double beta decays.

Recent developments in theoretical description of two-neutrino double beta decay

Some recent developments in the theoretical description of the two-neutrino double beta decay (2ν2β-decay) matrix elements are presented. We discuss the intermediate nucleus approach (INA), theS-matrix approach and the Operator Expansion Method (OEM), which offer different insight into the problem of 2ν2β-decay. From a detailed study within the OEM it follows that one of the basic features of 2ν2β-decay is the energy difference of the initial and final nuclei. The decisive role of the Coulomb interaction within the OEM is exhibited. The introduction of the time integral representation for the 2ν2β-decay matrix element, which is derived within the field theory approach, allows a more consistent analysis. It is shown that the results obtained within the INA in the quasiboson approximation scheme are questionable from the physics point of view and that higher order approximations are important. From a field theory analysis of the 2ν2β-decay amplitude it follows that the summation over the intermediate nuclear states corresponds to a summation over a class of meson exchange diagrams. A new electron-gamma exchange mechanism for 2ν2β-decay is proposed.

Effects of ρ exchange in coherent pion production

New theoretical calculations have been done that compare {pi}- and {rho}-exchange effects in exclusive coherent production of pions for {sup 12}C+{sup 12}C{r_arrow}{sup 12}C+{sup 12}C+{pi}{sup 0} below and above the pion threshold at incident energies of 100, 250, and 400 MeV/nucleon. Besides the important enhancement effects to the pion distributions due to the constructive coherence of {Delta}-hole and particle-hole terms describing the coherent, intermediate nuclear states of both projectile and target, additional effects have been observed due to the {rho}-exchange transition interaction. Calculations of the pion angular distributions, which are sensitive to the {rho}-exchange effect, are done that compare the ({pi}+{rho})-exchange effects to the {pi}-exchange effect alone. It is shown that at extreme angles, where the projectile scatters forward ({Theta}{sub P}=0{degree}), and the target scatters backward ({Theta}{sub T}=180{degree}), and the pion scattering forward or backward ({theta}{sub {pi}}=0{degree} or 180{degree}), that the {rho} amplitude is zero under the Born approximation. The insensitivity of the pion-energy distributions to {rho} exchange is also explained. It is shown that the {rho}-exchange effect is a rather mild one which affects only the midregion of the pion-angular distributions for the particular physical channels and incident energies considered here. {copyright} {ital 1998} {ital The American Physical Society}

Theoretical energy distributions around threshold from coherent pion production.

Detailed energy distributions have been calculated for exclusive [pi][sup 0] production in C+C collisions below and above threshold. The quantum-coherent, microscopic, many-body formalism used previously has been extended to include the [rho]-exchange as well as the [pi]-exchange interaction modified to produce nucleon isobars in the intermediate nuclear states. Analytic solutions to the [Delta]-hole and particle-hole coefficients using the degenerate, schematic-model approximation are used where collective-coherent, spin-isospin giant resonances are assumed for the nuclear excited states. The nuclear form factors that depend on these coefficients are solved analytically and become sums of degenerate [Delta]-hole and particle-hole states for given multipole angular momentum values of the excited nuclei. Also, in this approach, the overall amplitudes and differential cross sections for [pi][sup 0] production in either nucleus have been formally solved and the first numerical results of the pion, kinetic-energy distributions are presented.

Enhancement of the radiative channel in nuclear forward scattering

Two observations of nuclear forward scattering of Mossbauer radiation are presented. In one, a magnetic-resonance device was used to chop the γ-ray beam. After the beam was turned off, the nuclear target became a strong emitter of γ-rays in the forward direction. In the other observation, the energy of the intermediate excited nuclear state was changed suddenly by a hyperfine magnetic field reversal and the de-excitation of the nuclei occurred with the forward emission of γ-rays at the shifted frequency. In both cases, the enhancement of the radiative channel of nuclear scattering was observed.

Born-approximation amplitudes for pion production in heavy-ion collisions.

Formal solutions of the second-order amplitude in the Born approximation to the quantal, microscopic, many-body problem of pion production from the collision of equal-mass nuclei are presented where {Delta}-hole states are created in the intermediate nuclear states. The form factors containing nuclear structure information are solved in terms of particle-hole coefficients which describe any intermediate particle-hole state, regardless of whether it is coherent or incoherent. In this approach, the important tensor term has been included. A semiquantitative analysis is carried out which gives an indication of the approximate conditions under which pion production may be maximized under the excitation of {Delta}-hole states by the transition-spin, -isospin, one-pion-exchange interaction.

Nuclear response in electromagnetic quasi-free knockout including two-body currents

The nuclear response is considered for the outgoing nucleon knocked out in quasi-free scattering with polarized electrons. In the framework of the one-photon exchange approximation, the resulting five structure functions are calculated with an electromagnetic current of the target nucleus which includes two-body contributions coming from meson-exchange currents and isobar configurations in intermediate nuclear states. Specific calculations are presented for both proton and neutron knockout in the case of a 16O target nucleus. The sensitivity to final state interactions, mesonic effects and isobaric configurations is discussed.

Nucleon recoil polarization in electromagnetic quasi-free knockout including two-body currents

Polarization observables are considered for the outgoing nucleon knocked out in quasi-free electron scattering. The theoretical framework is based on the one-photon exchange approximation and the electromagnetic current of the target nucleus is built with one- and two-body contributions coming from meson-exchange currents and isobar configurations in intermediate nuclear states. Specific calculations are presented for both proton and neutron knockout, taking an 16O target nucleus as an example to set the scale for possible experiments. The sensitivity to final-state interactions, mesonic effects and isobaric configurations is discussed.