The Drawing or Why History Is Not Mathematics

The mystery of whether or not Werner Heisenberg gave Niels Bohr a drawing that Bohr came to believe was that of a German nuclear weapon, is discussed and resolved.     

Ionization potential of atoms and multiply charged ions versus the nuclear charge

The terms of ions and atoms are calculated with a method based on the Bohr model. The ionization potentials of helium-like, lithium-like, and beryllium-like ions are calculated as functions of the nuclear charge and electron quantum numbers. The results calculated are in satisfactory agreement with experimental data. The accuracy of the method is found to rise with the nuclear charge of ions.     

ON THE EDFORMATION OF THE EVEN-EVEN RARE-EARTH NUCLEI

Based on the approximate consideration suggested by Bohr and Mottelson,in which the moment of inertia is effected by paring correlation and depended on the deformation,the values of the nuclear deformation were extracted from the experimental effective moment of inertia,and it has been compared systematically with theoretical results and the values extracted from electronic quadrupole moment.It is shown that Bohr and Mottelson's consideration is reasonable.     

Quantization of Nuclear Octupole Vibration in the Parameter Space

In the framework of Bohr model, the quantized Hamiltonian based on nuclear nonaxial octupole deformation is derived in the'pararneter space, which is important to analyze the oscillating properties of atomic nucleus.     

A New Formula for the Spectra of Axial Symmetric and Transition Nuclei and a Quantity to Identify the Nuclear γ Deformation

The analytical limits of a speacial potential of the Bohr Hamiltonian are discussed in detail.A new formula for the axial symmetric,triakial deformed and the γ-soft nuclei is presented.The nuclear γ deformation can be identified with this formula.The calculations of some nuclear yrast lines seproduce the experiment al results very Well,and the degree of the nuclear γ deformation is obtained.     

Cosmology and a Living Cell

It is demonstrated that in the early stage of the Universe evolution, the space was in three different phase states: discontinuum, conventional continuum, and the Bohr compact set. Quantum mechanics in the Bohr compact set – the phase of space with the lowest symmetry – is developed here. Compound material objects were formed in it, in particular, living cells. It is demonstrated that in this phase, the angular momentum is not quantized, and the objects have a shell representing the Riemannian spherical surface. In this phase, the interaction potentials are unimportant, and reactions proceed extraordinary.     

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The present work is to calculate the magnetic thermodynamically functions, i.e. energy, the intensity of magnetization, enthalpy, entropy and Gibbs function for nuclear magnetic moments of T, D and neutron n at 2T and 1, 50, 100 and 150K from partition functions. It is shown that magnetic saturation of thermonuclear plasma does not easily occur for nuclear magneton is only of10^-3 of Bohr magneton. The work done by magnetic field is considerable.     

近玻尔速度氙离子激发钒的K壳层X射线

测量了2.4—6.0 MeV Xe~(20+)离子轰击V靶表面过程中辐射的X射线.计算了V的K壳层X射线发射截面,并将实验结果与平面波恩近似、ECPSSR、两体碰撞近似的理论计算进行了对比.讨论了近玻尔速度非对称碰撞过程中,BEA模型估算高电荷态重离子激发内壳层电离的修正因素.结果表明,综合考虑库仑偏转和有效电荷态修正后,BEA理论与实验结果符合较好.     

My Life in Nuclear Physics, Photography, and Opera

I sketch my life as an experimental nuclear physicist, beginning as a graduate student at Harvard University from 1948 to 1951, then as a postdoctoral fellow at the Cavendish Laboratory from 1951 to 1952, and finally as a faculty member at the University of Minnesota from 1952 until my retirement in 1991. I also carried out research at the Niels Bohr Institute in Copenhagen, Indiana University, and Los Alamos National Laboratory, and I participated in a number of summer schools and international conferences on nuclear physics. I also have worked in photography and opera. Over the years, I met and collaborated with many people in many walks of life who became friends for life.     

E0 transitional density for nuclei between spherical and deformed shapes

The Generator Coordinate Method (GCM) is used to construct the effective nuclear density operator suitable for calculations of E0 transitional densities with collective eigenfunctions of the phenomenological Bohr Hamiltonian. For example, the 0⁺ _gs \( \rightarrow\) 0⁺ ₂ transitional density is calculated for the shape-phase transitional nucleus ¹⁵⁰Nd using the eigenfunctions of the approximate X(5) solution of the Bohr Hamiltonian.     

Quantum Humor: The Playful Side of Physics at Bohr’s Institute for Theoretical Physics

From the 1930s to the 1950s, a period of pivotal developments in quantum, nuclear, and particle physics, physicists at Niels Bohr??s Institute for Theoretical Physics in Copenhagen took time off from their research to write humorous articles, letters, and other works. Best known is the Blegdamsvej Faust, performed in April 1932 at the close of one of the Institute??s annual conferences. I also focus on the Journal of Jocular Physics, a humorous tribute to Bohr published on the occasions of his 50^th, 60^th, and 70^th birthdays in 1935, 1945, and 1955. Contributors included Léon Rosenfeld, Victor Weisskopf, George Gamow, Oskar Klein, and Hendrik Casimir. I examine their contributions along with letters and other writings to show that they offer a window into some issues in physics at the time, such as the interpretation of complementarity and the nature of the neutrino, as well as the politics of the period.     

Derivation of a wave equation for collective motion

The generator coordinate method based on states derived from the random phase approximation, together with a strong assumption, leads to a differential equation for collective motion similar to the Bohr Hamiltonian with inertial parameters given by a formula related to the cranking model and with a potential almost equal to the ground state energy in the random phase approximation for each deformation.     

Nuclear pairing: New perspectives

Nuclear pairing correlations are known to play an important role in various single-particle and collective aspects of nuclear structure. After the first idea by A. Bohr, B. Mottelson, and D. Pines on similarity of nuclear pairing to electron superconductivity, S.T. Belyaev gave a thorough analysis of the manifestations of pairing in complex nuclei. The current revival of interest in nuclear pairing is connected to the shift of modern nuclear physics towards nuclei far from stability; many loosely bound nuclei are particle-stable only due to the pairing. The theoretical methods borrowed from macroscopic superconductivity turn out to be insufficient for finite systems such as nuclei, in particular, for the cases of weak pairing and proximity of continuum states. We suggest a simple numerical procedure of exact solution of the nuclear pairing problem and discuss the physical features of this complete solution. We show also how the continuum states can be naturally included in the consideration bridging the gap between the structure and reactions. The path from coherent pairing to chaos and thermalization and perspectives of new theoretical approaches based on the full solution of pairing are discussed.     

Paul Ehrenfest, Niels Bohr, and Albert Einstein: Colleagues and Friends

In May 1918 Paul Ehrenfest received a monograph from Niels Bohr in which Bohr had used Ehrenfest’s adiabatic principle as an essential assumption for understanding atomic structure. Ehrenfest responded by inviting Bohr, whom he had never met, to give a talk at a meeting in Leiden in late April 1919, which Bohr accepted; he lived with Ehrenfest, his mathematician wife Tatyana, and their young family for two weeks. Albert Einstein was unable to attend this meeting, but in October 1919 he visited his old friend Ehrenfest and his family in Leiden, where Ehrenfest told him how much he had enjoyed and profited from Bohr’s visit. Einstein first met Bohr when Bohr gave a lecture in Berlin at the end of April 1920, and the two immediately proclaimed unbounded admiration for each other as physicists and as human beings. Ehrenfest hoped that he and they would meet at the Third Solvay Conference in Brussels in early April 1921, but his hope was unfulfilled. Einstein, the only physicist from Germany who was invited to it in this bitter postwar atmosphere, decided instead to accompany Chaim Weizmann on a trip to the United States to help raise money for the new Hebrew University in Jerusalem. Bohr became so overworked with the planning and construction of his new Institute for Theoretical Physics in Copenhagen that he could only draft the first part of his Solvay report and ask Ehrenfest to present it, which Ehrenfest agreed to do following the presentation of his own report. After recovering his strength, Bohr invited Ehrenfest to give a lecture in Copenhagen that fall, and Ehrenfest, battling his deep-seated self-doubts, spent three weeks in Copenhagen in December 1921 accompanied by his daughter Tanya and her future husband, the two Ehrenfests staying with the Bohrs in their apartment in Bohr’s new Institute for Theoretical Physics. Immediately after leaving Copenhagen, Ehrenfest wrote to Einstein, telling him once again that Bohr was a prodigious physicist, and again expressing the hope that he soon would see both of them in Leiden.     

Hyperfine structure and \user1{g} factor measurements on Ba+ and Eu+ isotopes

Paul and Penning ion traps have been used to determine hyperfine structure coupling constants as well as nuclear $\user1{g} $ factors of Ba⁺ ions with great precision. Attempts are under way to measure both quantities for a long chain of Eu isotopes in order to determine differential hyperfine anomalies for a better understanding of the Bohr–Weisskopf effect.     

Niels Bohr and the dawn of quantum theory

Bohr’s atomic model, one of the very few pieces of physics known to the general public, turned a hundred in 2013: a very good reason to revisit Bohr’s original publications in the Philosophical Magazine, in which he introduced this model. It is indeed rewarding to (re-)discover what ideas and concepts stood behind it, to see not only ‘orbits’, but also ‘rings’ and ‘flat ellipses’ as electron trajectories at work, and, in particular, to admire Bohr’s strong belief in the importance of Planck’s law.     

Anomalous Internal Conversion as a Clue to Solving the <Superscript>209</Superscript>Bi Puzzle

A numerical analysis of the specific-difference (SD) method for eliminating the Bohr–Weisskopf effect in the theory of hyperfine splitting is performed within a more general theory of anomalous nuclear moments. The limiting accuracy of the SD method is demonstrated. In analyzing experimental data on the hyperfine splitting in H- and Li-like ions of ²⁰⁹Bi, it is found that the disagreement between theoretical and experimental results that was reported recently was due to going beyond this theoretical accuracy. Prospects of further experimental and theoretical studies in these realms are discussed.     

Decay and fission of oriented nuclei

The angular distributions of fragments originating from the binary decay of oriented spherical and deformed nuclei are investigated with allowance for correct transformation properties of wave functions under time inversion. It is shown that, as in the case of protonic decay, the adiabatic approximation for collective rotational degrees of freedom of the systems under investigation is inapplicable in describing the angular distributions of fragments of the deep-subbarrier alpha and cluster decays of nuclei. It is demonstrated that this approximation is justified in describing spontaneous and induced low-energy nuclear fission. The dependence of partial fission widths on the orientation of intrinsic axes, spins, and projections of spins and relative orbital angular momenta of fission fragments is analyzed by using the formalism of the unified theory of nuclear reactions and the theory of open Fermi systems. It is shown that the adiabatic approximation leads to the coherent interference between the wave functions for the relative motion of fragments, whereby the universal angular distributions of fission fragments of oriented nuclei is formed. Deviations from the A. Bohr formula are investigated for these distributions.