Hasil untuk "nucl-th"

Xabier Feal, Andrey Tarasov, Raju Venugopalan

We derived in arXiv:2206.04188 arXiv:2211.15712 a compact expression for the $N$-th rank QED polarization tensor $Π_{μ_1\cdots μ_N}(k_1,\cdots,k_N)$ in a $(0+1)$-dimensional worldline framework. This fully off-shell object, a function of $N$ external photon four-momenta, is a key ingredient in high-order computations of cusp anomalous dimensions and lepton anomalous magnetic moments. We demonstrate here that $Π_{μ_1\cdots μ_N}$ can further be expressed simply in terms of a small number of independent ``head" form factors (each representing $(N-1)!/2$ Feynman diagrams) which have a universal structure in terms of sums over fermion Green functions and (propertime derivative of) their boson worldline superpartners. This worldline representation bypasses explicit Wick contractions and avoids tensor reductions to scalar loop integrals à la Passarino and Veltman, order by order in perturbation theory. We give explicit expressions for the $4$-th and $6$-th rank head form factors and provide a computer script generalizing these results to arbitrary $N$ external photons. The multiplicity of heads, and their growth with $N$, can be understood in terms of orbits of the permutation group. We employ the Burnside-Cauchy-Frobenius lemma to show that it scales as $e^{N-1}/\sqrt{N}$ terms as opposed to the $e^{N-1} N!/\sqrt{N}$ terms in conventional perturbation theory. We reexpress worldline parameter integrals that define the $4$-th rank heads as Feynman parameter integrals to reproduce the seminal results by Karplus and Neuman for the on-shell light-by-light amplitude and extend these to the fully off-shell case in massless QED employing a tailored integration-by-parts procedure. In a follow-up paper, we will discuss the direct computation of worldline integrals, potentially providing a further $N!$ advantage relative to Feynman diagram computations at high orders in perturbation theory.

Zi-Rui Chen, Long-Jun Wang, Yuanbin Wu

$^{229}$Th, a crucial candidate for nuclear clocks and many other applications, is a typical heavy nucleus with an extremely low-energy isomeric state $^{229m}$Th. A detailed study of the nuclear structure of $^{229}$Th is performed here by the microscopic model of state-of-the-art projected shell model. Our calculation describes well low-energy levels of $^{229}$Th, and provides a reduced transition probability $B(M1)$ of $0.0240$ W.u. for the isomeric transition which agrees well with the radiative lifetime of $^{229m}$Th measured recently. Our result supports a small multipole mixing for the cross-band transition of the second-excited state of $^{229}$Th, suggesting that further investigations on the inconsistencies in the decay of the second-excited state should be necessary. The physics behind these properties is revealed by the analysis of the nuclear wave functions. Our findings provide a deep insight into $^{229}$Th from the microscopic nuclear structure point of view, and offer the chance for further studies for nuclear clocks and relevant topics by microscopic nuclear structure theory.

Y. Y. Huang, Q. Q. Cui, X. H. Wu et al.

The abundance ratios of radioactive elements U/Th and stable elements Pb/Os from the $r$-process are found to have a strong correlation. This correlation is quite robust with respect to astrophysical conditions. The U/Th-Pb/Os correlation is then applied to provide customized initial abundance ratios U/Th from the observed abundance ratios Pb/Os for six $r$-process enhanced metal-poor stars respectively. Ages of these six metal-poor stars are predicted by the U/Th chronometer, which are approximately between $11$ and $15$ Gyr. Their ages are compatible with the cosmic age of 13.8 billion years predicted from the cosmic microwave background radiation.

D. Filipescu, I. Gheorghe, S. Goriely et al.

New measurements of photofission and photoneutron reactions on $^{238}$U and $^{232}$Th in the Giant Dipole Resonance (GDR) energy region have been performed at the laser Compton-scattering $γ$-ray source of the NewSUBARU synchrotron radiation facility using a high-and-flat efficiency moderated $^3$He detection array. The neutron-multiplicity sorting of high-multiplicity fission neutron coincidence events has been performed using a dedicated energy dependent, multiple firing statistical treatment. The photoneutron $(γ,\,in)$ with $i$~=~1~--~3 and photofission $(γ,\,F)$ reactions have been discriminated by considering a Gaussian distribution of prompt-fission-neutron (PFN) multiplicities predicted by the theory of evaporation in sequential neutron emission from excited fission fragments. We report experimental $(γ,\,n)$, $(γ,\,2n)$, $(γ,\,3n)$ and $(γ,\,F)$ cross sections, average energies of PFNs and of $(γ,\,in)$ photoneutrons, as well as the mean number of PFNs per fission act and the width of the PFNs multiplicity distribution. Based on these primary experimental results and combined with reasonable assumptions, we extract also the first- and second-chance fission contributions. The new experimental results are compared with statistical-model calculations performed with the EMPIRE-3.2 Malta and TALYS-1.964 codes on the present data and with prompt fission emission calculations obtained with the Los Alamos model in the frame of the most probable fragmentation approach with and without sequential emission.

Jingyan Zhao, Adriana Pálffy, Christoph H. Keitel et al.

The nuclear isomeric state $^{229m}$Th with an exceptionally low excitation energy makes the $^{229}$Th isotope a crucial candidate for nuclear clocks and many other applications. Efficient and controllable production of $^{229m}$Th is essential and still remains a challenge. Here we report a novel approach for efficient production of $^{229m}$Th by the excitation of $^{229}$Th to the above-lying excited state at $29.19$ keV energy via the process of nuclear excitation by electron capture (NEEC). We show theoretically that the production rate of $^{229m}$Th per nucleus with accessible conditions can be six orders of magnitude larger than the value experimentally demonstrated using $29$-keV synchrotron radiation for this indirect excitation. With the efficient production of $^{229m}$Th, our results identify scenarios, as well as the characteristic NEEC signature with which NEEC events could be unambiguously identified, for a clear experimental identification of the long-sought NEEC phenomenon.

Yang-Yang Xu, Jun-Hao Cheng, You-Tian Zou et al.

In the present work, we investigate the excitation rates and population dynamics of $^{229}$Th nuclei induced by inelastic electron scattering, focusing on how electron energy, flux, and ionic charge state influence the excitation process of the nuclei. Using the Dirac Hartree-Fock-Slater method, we calculate cross sections for both the isomeric state (8.36 eV) and the second-excited state (29.19 keV) of $^{229}$Th over a wide range of ionic charge states and electron energies. Our results demonstrate that these factors significantly impact the nuclear excitation efficiency. The effect of indirect excitation through the second-excited state on enhancing the accumulation of nuclei in the isomeric state cannot be ignored. By applying rate equations to model the temporal evolution of nuclear populations, we show that under optimal conditions, up to 10\% of $^{229}$Th$^{4+}$ ions can be accumulated in the isomeric state. These findings provide important insights for optimizing electron-nucleus interactions, contributing to the development of $^{229}$Th-based nuclear clocks and relevant precision measurement applications.

Wu Wang, Xu Wang

A general quantum mechanical theory is developed for the isomeric excitation of $^{229}$Th in strong femtosecond laser pulses. The theory describes the tripartite interaction between the nucleus, the atomic electrons, and the laser field. The nucleus can be excited both by the laser field and by laser-driven electronic transitions. Numerical results show that strong femtosecond laser pulses are very efficient in exciting the $^{229}$Th nucleus, yielding nuclear excitation probabilities on the order of $10^{-11}$ per nucleus per pulse. Laser-driven electronic excitations are found to be more efficient than direct optical excitations.

V. A. Dzuba, V. V. Flambaum

We perform calculations of the energy shift of the nuclear clock transition frequency $^{229}$Th as a function of the number of electrons in Th ion. We demonstrate that the dependence of the nuclear frequency on electron configuration is significant. E.g., removing one electron from the atom leads to relative shift of the nuclear frequency $\sim 10^{-7}$, which is twelve orders of magnitude larger than expected relative uncertainty of the nuclear clock transition frequency ($\sim 10^{-19}$). This leads to difference of the nuclear clock frequencies in Th~IV, Th~III, Th~II and Th~I. The relative change of the nuclear frequency between neutral Th and its bare nucleus is 1\%. We also calculate the field shift constants for isotopic and isomeric shifts of atomic electron transitions in Th ions.

Hanxu Zhang, Wu Wang, Xu Wang

Nuclear excitation cross section of $^{229}$Th from the ground state to the low-lying isomeric state via inelastic electron scattering is calculated, on the level of Dirac distorted wave Born approximation. With electron energies below 100 eV, inelastic scattering is very efficient in the isomeric excitation, yielding excitation cross sections on the order of 10$^{-27}$ to 10$^{-26}$ cm$^2$. Systematic analyses are presented on elements affecting the excitation cross section, including the ion-core potential, the relativistic effect, the knowledge of the reduced nuclear transition probabilities, etc.

E. V. Tkalya, R. Si

A process of the decay of the anomalously low lying nuclear isomer $^{229m}$Th$(3/2^+,8.28 \pm 0.17$ eV) in the Thorium anion (Th$^-$) via the internal conversion (IC) channel is studied. We show that the half life of the nuclear isomer in the $6d_{3/2}^37s_{1/2}^2$ ground state and in the $6d_{3/2}^2 7s_{1/2}^2 7p_{1/2}^1$ excited state of Th$^-$ is $\approx1.5$ and $\approx1.1$ times bigger than in the $6d_{3/2}^2 7s_{1/2}^2$ ground state of the Th atom. The IC probabilities in the anion decreases despite the decay via the additional $6d_{3/2}$ or $7p_{1/2}$ electrons. This counterintuitive result is a consequence: a) of a decrease in the amplitudes of the $6d_{3/2}$ and $7s_{1/2}$ wave functions near the nucleus due to an increase in their diffuseness of upon the addition of extra electron, b) of mutual compensation in the IC probability due to a kinematic factor, which depends on the energy of the conversion electron in the continuum as $E_c^{-1/2}$, and the $E_c^{1/4}$ growth of the amplitudes of the electron wave functions.

Haruki Kurasawa, Toshio Suzuki

The relativistic expression for the $n$-th order moment of the nuclear charge density is presented. For the mean square radius(msr) of the nuclear charge density, the non-relativistic expression, which is equivalent to the relativistic one, is also derived consistently up to $1/M^2$ with use of the Foldy-Wouthuysen transformation. The difference between the relativistic and non-relativistic expressions for the msr of the point proton density is also discussed. The $n(\ge 4)$-th order moment of the nuclear charge density depends on the point neutron density. The 4-th order moment yields a useful information on the msr of the point neutron density, and is expected to play an important role in electron scattering off neutron-rich nuclei.

Nguyen Ngoc Anh, Nguyen Quang Hung, Nguyen Xuan Hai et al.

The level scheme of the compound $^{153}$Sm nucleus formed via the $^{152}$Sm($n_{th}$,$γ$) reaction is studied by using the $γ-γ$ coincidence spectrometer at Dalat Nuclear Research Institute, Vietnam. All the gamma cascades, which correspond to the decays from the compound state to 12 final levels of 0 ($\frac{3}{2}^+$), 7.535 ($\frac{5}{2}^+$), 35.844 ($\frac{3}{2}^-$), 90.875 ($\frac{5}{2}^-$), 126.412 ($\frac{1}{2}^-$), 127.298 ($\frac{3}{2}^-$), 182.902 ($\frac{5}{2}^-$), 321.113 ($\frac{3}{2}^+$), 404.129 ($\frac{1}{2}^-$), 405.470 ($\frac{3}{2}^-$), 414.924 ($\frac{1}{2}^+$), and 481.088 ($\frac{3}{2}^+$) keV, have been measured. A total number of 386 cascades corresponding to 576 gamma transitions has been detected. Among these cascades, 103 primary gamma transitions together with their corresponding intermediate levels and 299 secondary transitions have been determined. In addition, 29 primary gamma transitions, 42 intermediate levels, and 8 secondary transitions have been found to be the same as those extracted from the ENSDF data. The remain 74 primary gamma transitions, 61 intermediate levels, and 291 secondary transitions are therefore considered as the new data. In particular, based on an assumption that most of the transitions are dipole, we have tentatively assigned the unique spin value of $\frac{3}{2}\hbar$ for 53 observed intermediate levels corresponding to the cascades from the compound state to the final ones of 7.535 ($\frac{5}{2}^+$), 90.875 ($\frac{5}{2}^-$), and 182.902 ($\frac{5}{2}^-$) keV, whereas the remain levels are assigned with the spin values in the range of $[\frac{1}{2},\frac{3}{2}]\hbar$...

F. F. Karpeshin, M. B. Trzhaskovskaya, L. F. Vitushkin

Contemporary data are analyzed concerning the half-lives of the $^{229m}$Th isomer in neutral atoms and various ions. It is explicitly shown that the isomer lifetime may strongly depend on the plain environmental physical conditions like pressure and temperature. Calculation is performed on the united platform of interplay of traditional and subthreshold resonance conversion. General agreement with experiment is obtained in the cases of Th$^I$ and Th$^{III}$, a prediction is made concerning Th$^{IV}$. Disagreement with the experiment in the case of Th$^{II}$ may be a consequence of a random very sharp resonance with an electronic level. Account of the influence of the environment on the decay rate helps one to loose the resonance condition, which may lead to agreement with experiment. This will mean the first experimental observation of strong dependence of the nuclear decay rate on the environment.

E. V. Tkalya

The hyperfine splitting of the ground and low-energy $3/2^+(7.8 \pm 0.5$ eV) levels in the $^{229}$Th nucleus in muonic atom ($μ^-_{1S_{1/2}}{}^{229}$Th$)^*$ has been calculated considering the distribution of the nuclear magnetization in the framework of collective nuclear model with the wave functions of the Nilsson model for the unpaired neutron. It is shown that (a) the hyperfine splitting of the $3/2^+$ isomeric state is anomalously weak, and the reduction of hyperfine structure in comparison with the model of a point nuclear magnetic dipole is close to 100\%, (b) partial inversion of levels of the $^{229}$Th ground-state doublet and spontaneous decay of the ground state with excitation of the isomeric state take place, (c) the energy of the isomeric transition lies in the range of 120--140 eV, which makes possible the direct observation of the transition, registration of conversion electrons and measurement of the nuclear matrix element.

Bharat Kumar, S. K. Biswal, S. K. Singh et al.

The properties of recently predicted thermally fissile Th and U isotopes are studied within the framework of relativistic mean field (RMF) approach using axially deformed basis. We calculated the ground, first intrinsic excited state and matter density for highly neutron-rich thorium and uranium isotopes. The possible modes of decay like $α$-decay and $β$-decay are analyzed. We found that the neutron-rich isotopes are stable against $α$-decay, however they are very much unstable against $β$-decay. The life time of these nuclei predicted to be tens of second against $β$-decay. If these nuclei utilize before their decay time, a lots of energy can be produced within the help of multi-fragmentation fission. Also, these nuclei have a great implication in astrophysical point of view. The total nucleonic densities distribution are calculated, from which the clusters inside the parent nuclei are determined. %Most of the thorium isotopes are $α$ emitters, where as some %of them have short half-lives. In some cases, we found the isomeric states with energy range from 2 to 3 MeV and three minima in the potential energy surface of $^{228-230}$Th and $^{228-234}$U isotopes.

E V Tkalya, L P Yatsenko

A new method for obtaining of inverse population between quadrupole sublevels of the ground state $5/2^+(0.0)$ and the isomeric state $3/2^+(7.6$ eV) of the $^{229}$Th nucleus in a dielectric crystal with a large band gap by means of external source of the VUV radiation is proposed. The method is based on an efficient depopulation of the upper sublevels of the ground state of $^{229}$Th by resonant photons from narrowband laser or broader tunable free electron laser. Sublevels of the isomeric state play the role of intermediate states. In addition, we have considered a case of excitation of the isomeric state (without creation of inverse population) by broadband source of light with the anti-Stokes scattering. The proposed scheme of optical pumping results in (1) inverse population of nuclear sublevels without using extremely low temperatures, and (2) shows a new way for the creation of the gamma-ray laser of optical range at the nuclear transition in $^{229}$Th (a) in crystals with isovalent substitution of host ions (eg Si$^{4+}$ ions in the SiO$_2$ crystal replaced by the $^{229}$Th$^{4+}$ ions) and (b) in crystals such as Na$_2$ThF$_6$, where the substitution is not necessary.

K. Nomura, D. Vretenar, B. -N. Lu

A shape phase transition between stable octupole deformation and octupole vibrations in Th nuclei is analyzed in a microscopic framework based on nuclear density functional theory. The relativistic functional DD-PC1 is used to calculate axially-symmetric quadrupole-octupole constrained energy surfaces. Observables related to order parameters are computed using an interacting-boson Hamiltonian, with parameters determined by mapping the microscopic energy surfaces to the expectation value of the Hamiltonian in the boson condensate. The systematics of constrained energy surfaces and low-energy excitation spectra point to the occurrence of a phase transition between octupole-deformed shapes and shapes characterized by octupole-soft potentials.

Yaniv Shaposhnik, Eugene Shwageraus, Ezra Elias

Several reactivity control system design options are explored in order to satisfy shutdown margin (SDM) requirements in a high conversion BWRs operating in Th-233U fuel cycle (Th-RBWR). The studied has an axially heterogeneous fuel assembly structure with a single fissile zone sandwiched between two fertile blanket zones. The utilization of an originally suggested RBWR Y-shape control rod in Th-RBWR is shown to be insufficient for maintaining adequate SDM to balance the high negative reactivity feedbacks, while maintaining fuel breeding potential, core power rating, and minimum Critical Power Ratio (CPR). Instead, an alternative assembly design, also relying on heterogeneous fuel zoning, is proposed for achieving fissile inventory ratio (FIR) above unity, adequate SDM and meeting minimum CPR limit at thermal core output matching the ABWR power. The new concept was modeled as a single 3-dimensional fuel assembly having reflective radial boundaries, using the BGCore system, which consists of the MCNP code coupled with fuel depletion and thermo-hydraulic feedback modules.

Piotr Bozek, Iwona Wyskiel

This paper has been withdrawn by the authors, see P. Bozek and I. Wyskiel, arXiv: 1002.4999 [nucl-th]

D. T. Son

This is a comment on hep-th/0702136