Two Bessel Bridges Conditioned Never to Collide,Double Dirichlet Series,and Jacobi Theta Function

It is known that the moments of the maximum value of a one-dimensional conditional Brownian motion, the three-dimensional Bessel bridge with duration 1 started from the origin, are expressed using the Riemann zeta function. We consider a system of two Bessel bridges, in which noncolliding condition is imposed. We show that the moments of the maximum value is then expressed using the double Dirichlet series, or using the integrals of products of the Jacobi theta functions and its derivatives. Since the present system will be provided as a diffusion scaling limit of a version of vicious walker model, the ensemble of 2-watermelons with a wall, the dominant terms in long-time asymptotics of moments of height of 2-watermelons are completely determined. For the height of 2-watermelons with a wall, the average value was recently studied by Fulmek by a method of enumerative combinatorics.     

Spectroscopy of the 1S0-3P0 clock transition of 87Sr in an optical lattice

We report on the spectroscopy of the 5s(2) 1S0(F=9/2)-->5s5p 3P0(F=9/2) clock transition of 87Sr atoms (natural linewidth of 1 mHz) trapped in a one-dimensional optical lattice. Recoilless transitions with a linewidth of 0.7 kHz as well as the vibrational structure of the lattice potential were observed. By investigating the wavelength dependence of the carrier linewidth, we determined the magic wavelength, where the light shift in the clock transition vanishes, to be 813.5+/-0.9 nm.     

Ultrastable optical clock with neutral atoms in an engineered light shift trap

An ultrastable optical clock based on neutral atoms trapped in an optical lattice is proposed. Complete control over the light shift is achieved by employing the 5s(2) 1S0-->5s5p 3P0 transition of 87Sr atoms as a "clock transition." Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the clock transition indicate that the contribution of the higher-order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than 10(-17).     

Nuclear levels in 238Np

Low and high energy spectra from thermal neutron capture in ²³⁷Np have been studied over the energy ranges 25 to 650 keV and 2600 to 5500 keV. Primary transitions from neutron capture in four resonances have been observed between about 4800 and 5400 keV. Using 12 MeV deuterons, (d, p) spectra at three angles have been observed with a magnetic spectrograph. A nuclear level scheme for ²³⁸Np has been constructed by combining the results of the above measurements with previous data from a study of the ^242mAm α-decay. The Nilsson model has been used to interpret the level structure. Including results from the previous α-decay study, nine rotational bands can be assigned. The Nilsson configurations (K^π [Nn₃ΛΣ]) and band-head energies are: 2⁺π[642↑]?ν[631↓], 0.0 keV; 3⁺π[642↑]+ν[631↓], 86.6 keV; 3^?π[523↓]+ν[631↓], 136.0 keV; 2^?π[523↓]?ν[631↓], 182.8 keV; 5⁺π[642↑]+ν[622↑], 278.1 keV; 0⁺π[642↑]?ν[622↑], 332.5 keV; 5^?π[523↓]+ν[622↑], 342.6 keV; 0^?π[523↓]?ν[622↑], 286.0 keV; 6^?π[642↑]+ν[743↑], 301 keV. The measured (d, p) reaction cross sections are compared with theoretical calculations based on these assignments. The Gallagher-Moszkowski rule is found to be valid in the four cases where we have observed both parallel and antiparallel coupled bands with $\text{K}{}^{\mathrm{+}}\text{= Ω}{}_{\mathrm{<mtext>p</mtext>}}\text{+Ω}{}_{\mathrm{<mtext>n</mtext>}}$ and $\text{K}{}^{\mathrm{?}}\text{= |Ω}{}_{\mathrm{<mtext>p</mtext>}}\text{?Ω}{}_{\mathrm{<mtext>p</mtext>}}\text{|}$. The lowest levels of the two K = 0 bands have spin I = 1; Newby odd-even shifts can be determined in both cases.     

Production and decay of the isotope 271 Ds (Z = 110)

Production and decay of the isotope ²⁷¹Ds were studied. The isotope was produced by ²⁰⁸Pb + ⁶⁴Ni ²⁷¹Ds + n reaction. Fourteen -decay chains have been assigned to decays originating from the isotope ²⁷¹Ds. An excitation function of the production of this isotope was measured. The results have provided a good confirmation of production and decay of ²⁷¹Ds reported by Hofmann et al. The presence of an isomeric state in ²⁷¹Ds has been confirmed. The existence of a possible isomeric state in ²⁶⁷Hs is presented.Received: 22 September 2003, Revised: 26 December 2002, Published online: 10 August 2004PACS: 23.60. + e decay - 25.70.-z Low and intermediate energy heavy-ion reactions - 27.90. + b D. Kaji: Present address: Center for Nuclear Science, University of Tokyo, Wako-shi, Saitama 351-0198, Japan.A. Ozawa: Present address: University of Tsukuba, Tsukuba, Ibaragi 3058 577, Japan.