Evaporative cooling of helium nanodroplets with angular momentum conservation

Evaporative cooling of helium nanodroplets is studied with a statistical rate model that includes, for the first time, angular momentum conservation. While the final temperature of the droplets is almost identical to that previously predicted and later observed, the distribution of total droplet energy and angular momentum states is vastly more excited than a canonical distribution at the same temperature. It is found that the final angular momentum of the droplets is highly correlated with the initial direction, and that a significant fraction of the alignment of the total angular momentum should be transferred to the rotational angular momentum of an embedded molecule.     

Shell model theory of elastic scattering of nucleons by deformed nuclei

The escape width originating from a collective rotational state as a doorway state is calculated in the framework of the shell model theory of nuclear reactions. The rotational states are constructed by Yoccoz-Peierls angular momentum projection from deformed intrinsic states which are described by BCS wave functions. For some rare earth nuclei it is shown that there result escape widths of the order of magnitude of 20–100 keV.     

Investigation on phase and shape transitions in the hot rotating nucleus <Superscript>154</Superscript>Dy

A statistical theory for hot rotating nuclei incorporating deformation, collective and non-collective rotational degrees of freedom, shell effects and pairing correlations is used to investigate the occurrence of phase and shape transitions in the hot rotating deformed nucleus ¹⁵⁴Dy . The interplay of various degrees of freedom and their influence on the behavior of nuclei formed as fused compounds in heavy-ion reactions are studied. A phase transition from the superfluid to normal state in the nucleus with increasing temperature and angular momentum is observed. The effect of pairing on the level density parameter and nucleon separation energy has been analyzed and is found to be substantial. The neutron and proton separation energies extracted as a function of the angular momentum and temperature is found to decrease sharply for particular angular momentum states of the nucleus due to shape transitions from prolate collective to oblate non-collective at higher temperatures.     

Rotational states and interacting bosons

Rotational states are investigated in terms of the interacting boson model. A ground-state rotational band is built from a shell-model many-nucleon system. It is shown that the S and D collective nucleon pairs play dominant roles in low-spin states of the band and that this S-D dominance is broken in high-spin states. The intrinsic hamiltonian is constructed from the effective nucleon-nucleon interaction used in the shell model calculation and the intrinsic state of the rotational band is shown to be comprised primarily of S and D pairs. We introduce a λ boson which is a linear combination of s, d and higher angular momentum bosons, and the boson intrinsic state is given by the λ boson condensate state. The s and d bosons constitute approximately 90 % of the λ boson, and the boson intrinsic state reproduces very well the energy and the intrinsic quadrupole moment of the nucleon intrinsic state. The s-d boson hamiltonian is constructed from the S and D pairs, while effects of non S-D pairs are also included by renormalization of the boson hamiltonian. The renormalization is made by using the λ boson. The s-d boson quadrupole operator is derived similarly. The boson hamiltonian and quadrupole operator thus derived reproduce well the exactly calculated values for low-spin states of the rotational band, although the accuracy decreases in high-spin states. It is shown that the IBM possesses the same physical picture of the rotational states as the Nilsson scheme with pairing correlations. It is therefore concluded that the IBM is capable of describing low-lying rotational states.     

The angular momentum dependence of correlations in the ground state rotational spectra of20Ne and22Ne

Multi-Configuration-Hartree-Fock (MCHF) calculations with angular momentum projection before the variation of the internal degrees of freedom have been performed for the nuclei²⁰Ne and²²Ne. This procedure yields different correlated intrinsic states for the different members of a rotational band. Thus the angular momentum dependence of correlations has been studied. Experimentally, the ground state spectra of²⁰Ne and²²Ne show properties similar to the phase transitions observed in some rare earth nuclei which have been well reproduced through the present calculations. The calculated spectra andBE2-values show a significant improvement compared to the ones obtained by variation before the angular momentum projection is effected.     

Theoretical remarks for the analysis of electron scattering experiments on rotational nuclei

A convenient parametrization of longitudinal and transverse form factors of rotational nuclei is presented. This parametrization is model independent up to the order considered. It is intended to extract information on the intrinsic structure of ground state rotational bands by expressing the form factors for elastic and inelastic scattering within the band in terms of intrinsic charge and current multipoles, weighted by angular momentum dependent coefficients. The importance of the experimental measurements of transverse form factors is stressed as providing unique information on the distribution of the rotational current and hence, a unique test of the different rotational models. A qualitative comparison of three different models—rigid rotor, cranking and projected Hartree-Fock approach—is also presented in this context.     

Stability of nuclear rotational states

The stability of rotational states described by using a procedure of the Hartree-Fock-Bogoliubov method is discussed. The stability condition is obtained in a general form and some of its properties are examined with the aid of simplifying approximations. It is pointed out in conclusion that the Coriolis force might lead to the instability of rotational states for sufficiently large angular momenta. The instability of rotational states is caused by the instability of the pairing density, and also by that of the nuclear density distribution. In the former case it is shown that below the critical angular momentum, a first-order phase transition takes place and in some cases the rotational band breaks off. In the latter case, it might be considered that the assumption of an axially symmetric deformation is broken or large change of the equilibrium deformation is brought suddenly. Then discontinuous change of the rotational level might be seen at the unstable point.     

Atmospheric turbulence and orbital angular momentum of single photons for optical communication

The effects of propagation through random aberrations on coherence for single-photon communication systems based on orbital angular momentum states are quantified. A rotational coherence function is derived which leads to scattering equations for azimuthal modes of different orbital angular momentum states. The effect on a single-photon communication system is quantified using the channel capacity. The work shows that the decoherence effect of atmospheric turbulence on such systems is important even for weak turbulence.     

线型分子的电子能级之Λ分裂的新解释

认为电子态能级发生Λ分裂虽然是角动量引起的,但不是耦合而是运动牵连作用的结果.从这一认识出发,利用欧拉方程和拉格朗日方程分别得到了包含Λ分裂的分子转动哈密顿函数和哈密顿算符,所得结果与Van.Vleck的著名结论完全一致 关键词： Λ分裂 线型分子 欧拉方程 哈密顿算符     

Poincaré-sphere equivalent for light beams containing orbital angular momentum

The polarization state of a light beam is related to its spin angular momentum and can be represented on the Poincaré sphere. We propose a sphere for light beams in analogous orbital angular momentum states. Using the Poincaré-sphere equivalent, we interpret the rotational frequency shift for light beams with orbital angular momentum [Phys. Rev. Lett. 80, 3217 (1998)] as a dynamically evolving geometric phase.     

Monomer counterrotations and tunneling splitting in CO dimer by data of millimeter wave spectroscopy

Analysis of the rotational spectrum of the molecular dimer (CO)₂ measured in the millimeter wave range has been performed and four new rotational states are revealed. Three of these states are characterized by almost free rotations of both monomers in the dimer. These states have approximately the same first term σ in the expansion of the rotational energy in powers of the rotational angular momentum J for various values of the momentum projections on the dimer axis (K=0, 1, 2) and various rotational constants B. The intrinsic rotational angular momenta of CO dimers, j₁=j₂=1, are determined from the σ value. In addition, a state with K=2 is found which corresponds to one of the known shape isomers of (CO)₂. The values of the tunneling splitting for each of the new states are determined. The results indicate that previous data on the suppressed tunneling are determined by the asymmetry of internal rotations in the CO monomers rather than by the _K value.     

低振动激发HeI2分子振动预离解寿命和终转动态分布

用含时黄金规则波包法，对ＨｅＩ２分子在低初始振动激发（ｖ＜１２）态下振动预离解动力学作了全维量子力学计算。所预言的总衰变宽度和寿命与谱线宽和皮秒时间分解的实时态－态测量外推数据符合得相当好。计算的总衰变宽度对初始振动态ｖ是敏感的并呈现一种非线性关系。结果表明低振动激发ＨｅＩ２分子衰变模式仍应是量子力学的。除终态相互作用对决定终转动分布有重要作用以外，首次发现，低振动激发态的初始特性也能显著影响终转动态分布。用Ｉ２的转动常数对ｖ的关系合理地解释了这个独特现象     

量子N体系统的广义径向方程

介绍一种精确的方法 ,在质心坐标系中 ,把量子 N体系统的整体转动自由度和内部运动自由度完全地分离开来 .对于确定的轨道角动量状态 ,找到了一组完备且独立的角动量本征函数基 ,它们是坐标分量的齐次多项式 ,且满足 Laplace方程 .系统中的任何角动量本征函数都可以用这组函数基展开 ,组合系数只依赖于内部变量 ,称为广义径向函数 .可以简单且明显地推导出广义径向函数所满足的广义径向方程 .函数和方程式都只依赖于 (3 N- 6 )个内部变量 ,而且个数是有限的. A method without any approximation to separate the global rotational degrees of freedom in the Schrdinger equation for an N -body system completely from the internal ones is presented. For given orbital angular momentum states, we discover a complete set of independent base-functions, which are homogeneous polynomials in the components of the coordinate vectors and satisfy the Laplace equation. Any function with the given angular momentum and the given parity in the system can be...     

Alternative method for the measurement of the temperature of a Bose-Einstein condensate

Usually the temperature in a Bose-Einstein condensate is experimentally deduced resorting to the comparison between the Maxwell-Boltzmann velocity distribution function and the density profile in momentum space. Though a successful method it is merely an approximation, since it also implies the use of classical statistical mechanics at temperatures close to the condensation temperature where quantum effects play a relevant role and cannot be neglected. The present work puts forward an alternative method in which we use an ultra-intense light pulse and a nonlinear optical material as detectors for differences in times-of-flight, and in this way the temperature is deduced.     

Tight focusing of spirally polarized vortex beams

The tight focusing of spirally polarized focused vortex beams is analyzed numerically based on the vectorial Debye theory. The expressions for the electric field and the orbital angular momentum of focused beams are derived. It is shown that the intensity distribution in the focal plane is dependent on the specific spirally polarized state and the coefficient of the spiral polarization function. By presenting the phase contours of the component polarized in the radial direction, it is found that the radii of dislocation lines will increase with the increase of the power of the spirally polarization function. It is reveled that the same orbital angular momentum can be obtained for different spirally polarized state at certain distance along the propagation direction in the focal region. Besides, the orbital angular momentum distributions for different polarized states have fewer crossover points with each other for higher topological charge. The influence of the spirally polarized state on the orbital angular momentum in the focal plane is also studied.     

谐振子势与高斯势联合势阱中玻色爱因斯坦凝聚体的巨涡旋态

研究谐振子势与高斯势联合势阱中玻色爱因斯坦凝聚体的基态。发现凝聚体形成巨涡旋时,其涡旋个数等于平均角动量,且凝聚体密度分布和角动量密度分布相同,进而得到凝聚体形成巨涡旋时所处基态是角动量的本征态。发现势阱从各向同性的环形势阱逐渐变为各向异性的环形势阱的过程中,凝聚体的平均角动量与涡旋个数之比先由1平缓下降,然后迅速下降,最后保持在0.5附近。同时给出凝聚体密度分布和角动量分布的特征,并作出相应解释。     

High spin properties of 124Ba

The ¹²⁴Ba nucleus is investigated on the basis of the method of statistical mechanics by assuming the nucleons to move in triaxially deformed Nilsson potential. The variation in the Fermi energies of protons and neutrons is studied as a function of spin and temperature. The Fermi energies determined as a function of angular momentum is used to study the dependence of shell correction on angular momentum using the Strutinsky smoothing procedure. The most important observation is that the shell correction is almost the same for all spins for ¹²⁴Ba. The spin cutoff parameter and the single particle level density parameter are studied as a function of spin and temperature. Constant entropy lines drawn by plotting the excitation energy against angular momentum are found to be roughly at constant energy above the yrast line and are almost equally spaced. It is observed that no yrast traps are present for ¹²⁴Ba.     

Investigation of the cranking model wave function with respect to angular momentum

Projection of angular momentum on cranking model wave functions is performed for some simple cases. An extensive analysis has been possible since an algebraic projection technique is employed and a detailed numerical example is presented. The distribution of angular momentum as a function of rotational frequency and signature is analysed, and special attention is focused on the fact that the signature does not give any strict selection of angular momenta contained in the cranking wave function.