We discuss the problem of estimating uncertainties of the physical theories while keeping in mind the applications to nuclear structure. We present an analytical model which illustrates the ...present-day difficulties in achieving a satisfactory level of predictive power in nuclear structure theories as well as suggests the most important direction of improvements, required first of all on the level of the associated solution of the inverse problem of applied mathematics-as explained and illustrated in some detail in the text.
An exploratory experiment performed at REX-ISOLDE to investigate cluster-transfer reactions with radioactive beams in inverse kinematics is presented. The aim of the experiment was to test the ...potential of cluster-transfer reactions at the Coulomb barrier as a mechanism to explore the structure of exotic neutron-rich nuclei. The reactions 7Li(98Rb,αxn) and 7Li(98Rb,txn) were studied through particle-γ coincidence measurements, and the results are presented in terms of the observed excitation energies and spins. Moreover, the reaction mechanism is qualitatively discussed as a transfer of a clusterlike particle within a distorted-wave Born approximation framework. The results indicate that cluster-transfer reactions can be described well as a direct process and that they can be an efficient method to investigate the structure of neutron-rich nuclei at medium-high excitation energies and spins.
Cross sections and corresponding momentum distributions have been measured for the first time at zero degrees for the exotic nuclei obtained from a beam of 18O at 8.5 MeV/A impinging on a 1 ...mg/cm2238U target. Sizable cross sections were found for the production of exotic species arising from the neutron transfer and proton removal from the projectile. Comparisons of experimental results with calculations based on deep-inelastic reaction models, taking into account the particle evaporation process, indicate that zero degree is a scattering angle at which the differential reaction cross section for production of exotic nuclei is at its maximum. This result is important in view of the new generation of zero degrees spectrometers under construction, such as the S3 separator at GANIL, for example.
The γ-ray decay of excited states of the one-valence-proton nucleus 133Sb has been studied using cold-neutron induced fission of 235U and 241Pu targets, during the EXILL campaign at the ILL reactor ...in Grenoble. By using a highly efficient HPGe array, coincidences between γ-rays prompt with the fission event and those delayed up to several tens of microseconds were investigated, allowing to observe, for the first time, high-spin excited states above the 16.6 μs isomer. Lifetimes analysis, performed by fast-timing techniques with LaBr3(Ce) scintillators, revealed a difference of almost two orders of magnitude in B(M1) strength for transitions between positive-parity medium-spin yrast states. The data are interpreted by a newly developed microscopic model which takes into account couplings between core excitations (both collective and non-collective) of the doubly magic nucleus 132Sn and the valence proton, using the Skyrme effective interaction in a consistent way. The results point to a fast change in the nature of particle-core excitations with increasing spin.
The single closed-neutron-shell, one proton–hole nucleus 207Tl was populated in deep-inelastic collisions of a 208Pb beam with a 208Pb target. The yrast and near-yrast level scheme has been ...established up to high excitation energy, comprising an octupole phonon state and a large number of core excited states. Based on shell-model calculations, all observed single core excitations were established to arise from the breaking of the N=126 neutron core. While the shell-model calculations correctly predict the ordering of these states, their energies are compressed at high spins. It is concluded that this compression is an intrinsic feature of shell-model calculations using two-body matrix elements developed for the description of two-body states, and that multiple core excitations need to be considered in order to accurately calculate the energy spacings of the predominantly three-quasiparticle states.
In this paper we introduce a subjective notion of the predictive power of nuclear Hamiltonians (an objective one does not exist) and examine it in the particular context of the single-nucleon energy ...spectra. We consider various types of uncertainties originating both from the experiment and theory stressing the dominating character of the theoretical errors. The latter originate from the complexity of the nuclear many-body systems that is not matched adequately by the formalism behind the present day nuclear Hamiltonians. The related inverse problem is formulated and the presence of errors (ignorance, lack of knowledge) is parametrized in terms of the associated probability distributions. Various hypotheses concerning the input uncertainties ('numerical noise') are formulated and the impact of the input-uncertainties in the adjustment procedures down to the final parameter values and theoretical spectra is illustrated and discussed. A number of open problems are formulated and listed at the end of the paper.
We present examples and illustrate associated tests of statistical significance of the parameter fitting procedures in the nuclear mean-field context using a phenomenological toy-model based on the ...spherical Woods-Saxon Hamiltonian. We calculate the variance-covariance matrix and compare the standard estimates of the confidence intervals (and more generally – the uncertainty distributions) based on the standard χ2-fitting as opposed to a more general Monte-Carlo simulations. We give arguments for the superiority of the latter approach.
In this and the follow-up article we briefly discuss what we believe represents one of the most serious problems in contemporary nuclear structure: the question of statistical significance of ...parametrizations of nuclear microscopic Hamiltonians and the implied predictive power of the underlying theories. In the present Part I, we introduce the main lines of reasoning of the so-called Inverse Problem Theory, an important sub-field in the contemporary Applied Mathematics, here illustrated on the example of the Nuclear Mean-Field Approach.
High-spin states with the seniority v ≥ 2 have been investigated in the neutron-rich 118,120,122,124,126Sn isotopes. They were produced in fusion-fission processes following 48Ca + 208Pb, 48Ca + 238U ...reactions and via fission of target nuclei in the 64Ni + 238U system. By employing techniques of delayed- and cross-coincidences, it was possible to establish level schemes up to an 8 MeV excitation energy. The 13− and 15− states were identified as being isomeric and their half-lives were determined. The reduced transition probabilities extracted for isomeric transitions behave very regularly with the mass number A. The spin-parity values assigned to or suggested for the identified states were supported by shell-model calculations and by systematics.
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