Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases

We use the nonperturbative linear \delta expansion method to evaluate analytically the coefficients c_1 and c_2^{\prime \prime} which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by T_c= T_0 \{1 + c_1 a n^{1/3} + [ c_2^{\prime} \ln(a n^{1/3}) +c_2^{\prime \prime} ] a^2 n^{2/3} + {\cal O} (a^3 n)\}, where T_0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c_1 to order-\delta^2 with the result c_1= 3.06. Here, we push the calculation to the next two orders obtaining c_1=2.45 at order-\delta^3 and c_1=1.48 at order-\delta^4. Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c_2^{\prime\prime}=101.4, c_2^{\prime \prime}=98.2 and c_2^{\prime \prime}=82.9. Our analytical results seem to support the recent Monte Carlo estimates c_1=1.32 \pm 0.02 and c_2^{\prime \prime}= 75.7 \pm 0.4.Comment: 29 pages, 3 eps figures. Minor changes, one reference added. Version in press Physical Review A (2002

Calculating Casimir Energies in Renormalizable Quantum Field Theory

Quantum vacuum energy has been known to have observable consequences since 1948 when Casimir calculated the force of attraction between parallel uncharged plates, a phenomenon confirmed experimentally with ever increasing precision. Casimir himself suggested that a similar attractive self-stress existed for a conducting spherical shell, but Boyer obtained a repulsive stress. Other geometries and higher dimensions have been considered over the years. Local effects, and divergences associated with surfaces and edges have been studied by several authors. Quite recently, Graham et al. have re-examined such calculations, using conventional techniques of perturbative quantum field theory to remove divergences, and have suggested that previous self-stress results may be suspect. Here we show that the examples considered in their work are misleading; in particular, it is well-known that in two dimensions a circular boundary has a divergence in the Casimir energy for massless fields, while for general dimension $D$ not equal to an even integer the corresponding Casimir energy arising from massless fields interior and exterior to a hyperspherical shell is finite. It has also long been recognized that the Casimir energy for massive fields is divergent for $D\ne1$. These conclusions are reinforced by a calculation of the relevant leading Feynman diagram in $D$ and three dimensions. There is therefore no doubt of the validity of the conventional finite Casimir calculations.Comment: 25 pages, REVTeX4, 1 ps figure. Revision includes new subsection 4B and Appendix, and other minor correction

Exact conserved quantities on the cylinder I: conformal case

The nonlinear integral equations describing the spectra of the left and right (continuous) quantum KdV equations on the cylinder are derived from integrable lattice field theories, which turn out to allow the Bethe Ansatz equations of a twisted ``spin -1/2'' chain. A very useful mapping to the more common nonlinear integral equation of the twisted continuous spin $+1/2$ chain is found. The diagonalization of the transfer matrix is performed. The vacua sector is analysed in detail detecting the primary states of the minimal conformal models and giving integral expressions for the eigenvalues of the transfer matrix. Contact with the seminal papers \cite{BLZ, BLZ2} by Bazhanov, Lukyanov and Zamolodchikov is realised. General expressions for the eigenvalues of the infinite-dimensional abelian algebra of local integrals of motion are given and explicitly calculated at the free fermion point.Comment: Journal version: references added and minor corrections performe

Structure of Fe 70: Single-particle and collective degrees of freedom

Excited states in the neutron-rich Fe70 nucleus were populated in a one-proton removal reaction from Co71 projectiles at 87 MeV/nucleon. A new transition was observed with the γ-ray tracking array GRETINA and shown to feed the previously assigned 41+ state. In comparison to reaction theory calculations with shell-model spectroscopic factors, it is argued that the new γ ray possibly originates from the 61+ state. It is further shown that the Doppler-reconstructed γ-ray spectra are sensitive to the very different lifetimes of the 2+ and 4+ states, enabling their approximate measurement. The emerging structure of Fe70 is discussed in comparison to LNPS-new large-scale shell-model calculations

Cross-shell excitations in Si 31

The Si31 nucleus was produced through the O18(O18, αn) fusion-evaporation reaction at Elab=24MeV. Evaporated α particles from the reaction were detected and identified in the Microball detector array for channel selection. Multiple γ-ray coincidence events were detected in Gammasphere. The energy and angle information for the α particles was used to determine the Si31 recoil kinematics on an event-by-event basis for a more accurate Doppler correction. A total of 22 new states and 52 new γ transitions were observed, including 14 from states above the neutron separation energy. The positive-parity states predicted by the shell-model calculations in the sd model space agree well with experiment. The negative-parity states were compared with shell-model calculations in the psdpf model space with some variations in the N=20 shell gap. The best agreement was found with a shell gap intermediate between that originally used for A≈20 nuclei and that previously adapted for P32,34. This variation suggests the need for a more universal cross-shell interaction

Intruder configurations of excited states in the neutron-rich isotopes P 33 and P 34

Excited states in the neutron-rich isotopes P33 and P34 were populated by the O18+O18 fusion-evaporation reaction at Elab=24 MeV. The Gammasphere array was used along with the Microball particle detector array to detect γ transitions in coincidence with the charged particles emitted from the compound nucleus S36. The use of Microball enabled the selection of the proton emission channel. It also helped in determining the exact position and energy of the emitted proton; this was later employed in kinematic Doppler corrections. 16 new transitions and 13 new states were observed in P33 and 21 γ rays and 20 energy levels were observed in P34 for the first time. The nearly 4π geometry of Gammasphere allowed the measurement of γ-ray angular distributions leading to spin assignments for many states. The experimental observations for both isotopes were interpreted with the help of shell-model calculations using the (0+1)ω PSDPF interaction. The calculations accounted for both the 0p-0h and 1p-1h states reasonably well and indicated that 2p-2h excitations might dominate the higher-spin configurations in both P33 and P34

Multi-intruder structures in 34P

The available experimental information on 34P has been greatly increased through the analysis of γ decays in coincidence with protons from the interaction of an 18O beam at 24 MeV with an 18O target. Light charged particles from the reaction were detected with Microball, and multiple γ-ray coincidences with Gammasphere. Many observed γ transitions have been identified and placed in the level scheme. Additionally, for most states, spins have been assigned based on measured γ-ray angular distributions while parities were inferred from lifetimes determined through Doppler-broadened line-shape analysis. Most of the states observed have been interpreted in terms of shell-model calculations using the WBP-a and SDPF-NR interactions having one particle in the 0f7/2 or 1p3/2 orbital. The two calculations agree almost equally well with the data resulting in root-mean-square differences of about 200 keV. However, a few high-lying states observed with long lifetimes challenge current calculations. Two of these may be associated with stretched πf7/2⊗νf7/2 states, but the calculations overpredict their energies by 2-3 MeV. Furthermore, a long-lived 7919-keV state is established for which no explanation is available at present

The polarization sensitivity of GRETINA

Compton polarimeters have played an important role in the study of nuclear structure physics, but have often been limited in their applications because of relatively low γ-ray detection efficiency. With the advent of γ-ray tracking detector arrays, which feature nearly 4π solid angle coverage and the ability to identify the location of Compton-scattering events to within a few millimeters, this limitation can be overcome. Here we present a characterization of the performance of the Gamma Ray Energy Tracking In-beam Nuclear Array (GRETINA) as a Compton polarimeter using the 24Mg(p,p′) reaction at 2.45 MeV proton energy. We also discuss a new capability added to the simulation package UCGretina to simulate the emission of polarized photons, and compare it to the measured data. Finally, we use these simulations to predict the performance of the Gamma Ray Energy Tracking Array (GRETA)

Calculated phase diagrams, iron tolerance limits, and corrosion of Mg-Al alloys

The factors determining corrosion are reviewed in this paper, with an emphasis on iron tolerance limit and the production of high-purity castings. To understand the iron impurity tolerance limit, magnesium phase diagrams were calculated using the Pandat software package. Calculated phase diagrams can explain the iron tolerance limit and the production of high-purity castings by means of control of melt conditions; this is significant for the production of quality castings from recycled magnesium. Based on the new insight, the influence of the microstructure on corrosion of magnesium alloys is reviewed

The deformed 0+ state in 34Si

The energy of the lowest deformed 2-particle 2-hole (2p2h) 0+ state in even-even N = 20 nuclei is a key observable directly related to the size of the neutron N = 20 shell closure. 34Si, with 14 protons and 20 neutrons, lies at the boundary of the "island of inversion", where the deformed 2p2h 0+ state is the ground state in even-A nuclei. In 34Si, the 2p2h 0+ state is expected to be particularly low lying - in some theories it is even predicted to lie below the first 2 + state. While there have been a number of attempts, using various techniques, no experiment to date has been able to firmly locate the 34Si 2p2h 0+ state although a number of candidates have been suggested. Here we present, for the first time, data obtained from a fusion-evaporation reaction 18O(18O, 2p) to produce 34Si. Gammasphere and Microball were used to detect γ-γ coincidences and charged particles (two protons), respectively. The increased sensitivity of this experiment using γ-γ coincidences and a high charged-particle detection efficiency helped to exclude previously reported candidates and provided a stringent limit on the anticipated γ decay from the first 2+ state to the 2p2h 0+ state