CHEMICAL POTENTIAL QUANTIZATION AND BOSE-EINSTEIN CONDENSATION

In this paper, first of all, we proved if the ideal Bose gas with a finite volume and number of particles has a non-degenerate single-particle energy level ε_n, the chemical potential μ can take the value μ_n=ε_n and there is a phase transition temperature T_p,n, where n=0,1,2… Taking ε₀≤ε_n<ε_n+1, then T_p,0≥T_p,n>T_p,n+1. When the temperature T>T_p,n or T≤T_p,n+1, μ≠ε_n and the most probable occupation number N_n=0. In the temperature interval T_p,n≥ T>T_p,n+1,μ=ε_n and 0≤N_n=N-Σ_jN_j<～supN_n, where N_j is the most probable occupation number in the degenerate level j. Thus, if the finite ideal Bose gas has some non-degenerate single-particle levels, there exists a characteristic temperature T_p=T_p,0. The chemical potential μ is quantized when T≤T_p, and this leads to the creation of a macroscopic quantum state (pure state) or Bose-Einstein condensation phase. T_p=T_p,0 is a first-order phase transition point, T_p,n≠0 is a zero-order phase transition point. Next, we obtained a new expression of the most probable distribution of the finite ideal Bose gas. In this expression N_j is directly proportional to g_j-1, where g_j and N_j are, respectively, the degeneracy and the most probable occupation number in the degenerate level j. This property agrees with what chemical potential can be quantized if there is a non-degenerate level for the finite ideal Bose gas. Finally, using this expression, we defined a micro-partition function M, obtained the statistical expressions of some thermodynamical quantities.     

Formation of high-T c phases of the system Bi-Pb-Sr-Ca-Cu-O in a fluxed KCl melt

The influence of the conditions of synthesis and annealing on the ratio of the volumes and the temperature T _c ⁿ at which transition to the superconducting state begins is investigated on the basis of diamagnetic susceptibility measurements and x-ray phase analysis for bismuth 2212 and 2223 phases obtained from solution in a KCl melt. It is found that the value of T _c ⁿ for the 2212 phase decreases as the temperature and the holding time are increased in synthesis. The 2212–2223 transition in the fluxed KCl melt takes place in the presence of an oxygen deficiency, and the width of the transition interval to the superconducting state of the 2223 phase depends on the cooling rate of the fluxed melt after isothermal holding and also on subsequent annealing in air. Temperatures T _c ⁿ =107 K, 90 K, and 20 K are observed for unannealed crystals of the 2223 phase with average dimensions 50×50 μm. Air annealing leads to oxygen saturation of their lattice, and T _c ⁿ =107 K throughout the entire structure of the crystal. Fiz. Tverd. Tela (St. Petersburg) 39, 1761–1763 (October 1997)     

Dephasing time of a positron accelerated by a laser pulse

The dephasing time of a positron in the total field associated with a laser pulse in a plasma J28is studied numerically. It is shown that the dynamics of the positron is quite different from that of an electron due to the electrostatic potential in the body of the pulse. The dephasing time of the positron increases with the pulse length and decreases with the pulse intensity nonlinearly. In the long pulse case (L》λ_p) the dephasing time is proportional to the pulse length. These results provide a scientific basis for experiments to observe the positron acceleration scheme, and may be important to the physics of laser-article interactions in multi-component plasmas.     

Nuclear spin-lattice and nuclear spin-spin relaxation time measurements in EuB6 at low temperatures using the spin-echo technique

Experimental results on the nuclear spin-lattice and nuclear spin-spin relaxation times in the ferromagnetic EuB₆ at temperatures below 4·2 K are presented using the external magnetic field,H _ext, in the range of 0 ⩽H _ext ⩽ 10 kG. Nuclear spin-spin relaxation time computed on the basis of the Suhl-Nakamura process turns out to be 3·2μs, which compares well with the experimental value 11·1μs obtained with the 10 kG magnetic field at 1·7 K. It is found that in the ferromagnetic EuB₆,T ₁ is approximately 5 × 10³ times larger thanT ₂ at 1·7 K with the 10 kG magnetic field. Thus the effect ofT ₁ onT ₂ can be neglected. From the experimental value ofT ₂, the value of the homogeneous line broadening is found to be 14 kHz. The corresponding value obtained from the cw method is 175 kHz. This evidently shows the presence of the inhomogeneous line broadening in the cw NMR.     

RADIATION-INDUCED DEFECTS IN RADIATION HARD AND SOFT OXIDES

The point defects of P_b and E′ in radiation hard and soft Si-SiO₂ samples were examined using electron spin resonance (ESR). The experimental results showed that these defects were correlated with the ways of oxidation process, the dosage of ⁶⁰Co radiation and the radiation bias field. Besides, the ΔH (peak of peak) of P_b and E′ indicated that P_b is the defect with slow electron spin relaxation time while E′ is the defect with fast electron spin relaxation time. Finally, the experimental results are explained qualitatively.     

Historical overview and introduction

The complex balance of processes occurring at the cascade of exotic H-atoms is usually described by the so-called standard cascade model, but this model neglects variations of the kinetic energy T of the exotic atom during the cascade which are crucial for the analysis of several important experiments. New experimental results on T _μp at H₂ pressures between 0.063 and 4 hPa demonstrate the importance of acceleration due to Coulomb de-excitation processes at highly excited μp levels n > 9. The data at the lowest density are sensitive to the initial values of the kinetic energy and n-levels at the moment of atomic capture. From the measured low-energy tail of the T _μp-distribution it can be concluded that a considerable part of the μp(2s) atoms is metastable at pressures of a few hPa. This revised version was published online in August 2006 with corrections to the Cover Date.     

INFLUENCE OF OXYGEN UPON THE SUPERCONDUCTIVITY OF THE Pb-DOPED 2223 SUPERCONDUCTOR

The influences of oxygen content (by quenching from different temperatures in air or oxygen) and its re-distribution (by annealing in nitrogen at 200℃) on T_c and room temperature resistivity were studied. It was found that T_c as a function of oxygen content or charge carrier concentration exhibits a maximum. Upon oxygen re-distribution, the room temperature resistivity would always inclose but T_c would change in a complicated way. T_c increases for the oxygen-rich state and decreases for the oxygen-deficient state Internal friction measurements showed that there are two kinds of oxygen defects in the Bi₂-O₂ layers. One is the isolated oxygen interstitials and the other is oxygen vacancies on the excess oxygen chains. It is proposed that the isolated interstitial oxygen will produce a set of impurity states near the Fermi level, and will create holes on the Cu3d-O2p band through charge transfer from the Cu3d-O2p band to the impurity states. The content of the isolated oxygen interstitial is believed to be the major factor for determining the charge carrier concentration. Variation of T_c and room temperature resistivity with oxygen re-distribution is sat-isfactorily explained as to be induced by combination of oxygen interstitials with oxygen vacancies on the excess oxygen-chains.     

EFFECTIVE POTENTIAL OF λφ41+3 AT ZERO AND FINITE TEMPERATURES

The effective potential of λφ⁴₁₊₃ model with both signs of parameter m² is evaluated at T=0 by means of a simple but effective method for regularization and renormalization. Then at T≠0, the effective potential is evaluated in imaginary time Green function approach, using the Plana formula. A critical temperature for restoration of symmetry breaking in the standard model of particle physics is estimated to be T_c≌510 GeV.     

超快二维红外光谱用于研究单体水分子中的直接振动能量传递

Vibrational relaxation dynamics of monomeric water molecule dissolved in d-chloroform solution were revisited using the two dimensional Infrared (2D IR) spectroscopy. The vibrational lifetime of OH bending in monomeric water shows a bi-exponential decay. The fast component (T₁=(1.2±0.1) ps) is caused by the rapid population equilibration between the vibrational modes of the monomeric water molecule. The slow component (T₂=(26.4±0.2) ps) is mainly caused by the vibrational population decay of OH bending mode. The reorientation of the OH bending in monomeric water is determined with a time constant of τ=(1.2±0.1) ps which is much faster than the rotational dynamics of water molecules in the bulk solution. Furthermore, we are able to reveal the direct vibrational energy transfer from OH stretching to OH bending in monomeric water dissolved in d-chloroform for the first time. The vibrational coupling and relative orientation of transition dipole moment between OH bending and stretching that effect their intra-molecular vibrational energy transfer rates are discussed in detail.     

LOW-FREQUENCY INTERNAL FRICTION STUDY FOR SrBi2Ta2O9 FERROELECTRIC CERAMICS

Low-frequency internal friction (IF) of SrBi₂Ta₂O₉(SBT) ceramics has been measured at temperatures ranging from 293 to 623 K. Two IF peaks, with their locations around 393 K (P1) and 569 K (P2) (f≈1.58 Hz), respectively, are observed. P1 is found to be associated with a relaxation process with activation energy of 0.97 eV and pre-exponential factor of 3.58×10^-14 s. Peak shape analyses reveal that P1 can be well described by a broadened Debye peak with the width parameter β from 2.70 to 2.92. The mechanism responsible for P1 is proposed to be relaxation of oxygen vacancies near domain walls(DWs). P2 is considered to arise from viscous motion of DWs since it shows characteristics of static hysteresis type. Comparisons for the IF behavior between SBT and Pb(Zr, Ti)O₃(PZT) suggest that in SBT oxygen vacancies are much less localized near DWs than that in PZT. This result provides a possible explanation for the weak DW pinning due to oxygen vacancies in SBT.     

A New Approach of Two-Dimensional the NMR Relaxation Measurement in Flowing Fluid

Driven-equilibrium fast saturation recovery (DEFSR), as a new method for two-dimensional (2-D) nuclear magnetic resonance (NMR) relaxation measurement based on pulse sequence in flowing fluid, is proposed. The two-dimensional functional relationship between the ratio of transverse relaxation time to longitudinal relaxation time of fluid (T ₁/T ₂) and T ₁ distribution is obtained by means of DEFSR with only two one-dimensional measurements. The rapid measurement of relaxation characteristics for flowing fluid is achieved. A set of the down-hole NMR fluid analysis system is independently designed and developed for the fluid measurement. The accuracy and practicability of DEFSR are demonstrated.     

Optimal echo spacing for multi-echo imaging measurements of Bi-exponential T2 relaxation

Calculations, analytical solutions, and simulations were used to investigate the trade-off of echo spacing and receiver bandwidth for the characterization of bi-exponential transverse relaxation using a multi-echo imaging pulse sequence. The Cramer–Rao lower bound of the standard deviation of the four parameters of a two-pool model was computed for a wide range of component T₂ values and echo spacing. The results demonstrate that optimal echo spacing (TE_opt) is not generally the minimal available given other pulse sequence constraints. The TE_opt increases with increasing value of the short T₂ time constant and decreases as the ratio of the long and short time constant decreases. A simple model of TE_opt as a function of the two T₂ time constants and four empirically derived scalars is presented.     

Emulation of petroleum well-logging D-T2 correlations on a standard benchtop spectrometer

An experimental protocol is described that allows two-dimensional (2D) nuclear magnetic resonance (NMR) correlations of apparent diffusion coefficient D_app and effective transverse relaxation time T_2,eff to be acquired on a bench-top spectrometer using pulsed field gradients (PFG) in such a manner as to emulate D_app − T_2,eff correlations acquired using a well-logging tool with a fixed field gradient (FFG). This technique allows laboratory-scale NMR measurements of liquid-saturated cored rock to be compared directly to logging data obtained from the well by virtue of providing a comparable acquisition protocol and data format, and hence consistent data processing. This direct comparison supports the interpretation of the well-logging data, including a quantitative determination of the oil/brine saturation. The D − T₂ pulse sequence described here uses two spin echoes (2SE) with a variable echo time to encode for diffusion. The diffusion and relaxation contributions to the signal decay are then deconvolved using a 2D numerical inversion. This measurement allows shorter relaxation time components to be probed than in conventional diffusion measurements. A brief discussion of the numerical inversion algorithms available for inverting these non-rectangular data is included. The PFG-2SE sequence described is well suited to laboratory-scale studies of porous media and short T₂ samples in general.     

In vivo NMR T2 relaxation of experimental brain tumors in the cat: A multiparameter tissue characterization

Experimental gliomas (F98) were inoculated in cat brain for the systematic study of their in vivo T₂ relaxation time behavior. With a CPMG multi-echo imaging sequence, a train of 16 echoes was evaluated to obtain the transverse relaxation time and the magnetization M(0) at time t = 0. The magnetization decay curves were analyzed for biexponentiality. All tissues showed monoexponential T₂, only that of the ventricular fluid and part of the vital tumor tissue were biexponential. Based on these NMR relaxation parameters the tissues were characterized, their correct assignment being assured by comparison with histological slices. T₂ of normal grey and white matter was 74 ± 6 and 72 ± 6 msec, respectively. These two tissue types were distinguished through M(0) which for white matter was only 0.88 of the intensity of grey matter in full agreement with water content, determined from tissue specimens. At the time of maximal tumor growth and edema spread a tissue differentiation was possible in NMR relaxation parameter images. Separation of the three tissue groups of normal tissue, tumor and edema was based on T₂ with T_2(normal) < T_2(tumor) < T_2(edema). Using M(0) as a second parameter the differentiation was supported, in particular between white matter and tumor or edema. Animals were studied at 1–4 wk after tumor implantation to study tumor development. The magnetization M(0) of both tumor and peritumoral edema went through a maximum between the second and third week of tumor growth. T₂ of edema was maximal at the same time with 133 ± 4 msec, while the relaxation time of tumor continued to increase during the whole growth period, reaching values of 114 ± 12 msec at the fourth week. Thus, a complete characterization of pathological tissues with NMR relaxometry must include a detailed study of the developmental changes of these tissues to assure correct experimental conditions for the goal of optimal contrast between normal and pathological regions in the NMR images.     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

MRICOM–MRI COntrast Modelling using 2D T1–T2 correlation spectra and relaxation signatures

Image contrast is calculated by inputting experimental 2D T₁–T₂ relaxation spectra into the ODIN software interface. The method involves characterising a magnetic resonance imaging pulse sequence with a “relaxation signature” which describes the sensitivity of the sequence to relaxation and is independent of sample parameters. Maximising (or minimising) the overlap between the experimental 2D T₁–T₂ relaxation spectra and the relaxation signature can then be used to maximise image contrast. The concept is illustrated using relaxation signatures for the echo planar imaging and Turbo spin-echo imaging sequences, together with in-vitro 2D T₁–T₂ spectra for liver and cartilage.     

14N pulsed nuclear quadrupole resonance. 3. Effect of a pulse train. Optimal conditions for data averaging

The calculations developed in this paper aim at determining the optimal conditions of a NQR experiment when a transition is monitored by means of a pulse train with pulses of identical duration and signal acquisition after each pulse; coherences are assumed to vanish by effective transverse relaxation prior to every new pulse. These calculations demonstrate that, as in NMR, a steady state is effectively reached for any value of the recycle time. However, by contrast with NMR, it is shown that, for optimal data averaging under steady state conditions, the recycle time T can be kept as low as possible (the only limitation is the acquisition time). Nutation curves (signal amplitude versus pulse length) calculated in the steady state case are shown to depend strongly on the ratio T/T ₁ (T ₁: longitudinal relaxation time). The signal growth as a function of T/T ₁under averaging of the first transients has been evaluated as well as the number of pulses necessary for reaching a steady state.     

Saving transverse magnetization

A magnetization storage sequence, ALT-1 (alternating longitudinal and transverse components), is reported. The ALT-1 sequence is a hybrid of two types of storage sequences, the Carr–Purcell type and store-and-restore sequences. During incremental storage periods within the ALT-1 sequence, essentially half of the initially transverse magnetization is stored along the z-axis and the other half is prolonged by an echo-generating pulse. The portions of initial magnetization that are stored as longitudinal components or transverse components are alternated by a π/2 pulse during the cycle. Both transverse components of the initial magnetization are treated the same in the ALT-1 sequence and orientational (phase) information of the initial magnetization is kept during the storage period. The ALT-1 sequence can preserve magnetization more effectively than a published class of modified Carr–Purcell type sequences, because essentially half of the magnetization during incremental storage periods is not subjected to relaxation from T₂ effects.     

Multiple quantum coherences: New NMR tools to study materials and living systems

Intermolecular multiple-quantum coherences have been proven in recent years to provide a novel contrast mechanism to study heterogeneity in liquid systems. This subject represents a source of remarkable interest in the fields of physics of matter and biomedicine. Recent results achieved on intermolecular double-quantum signal transverse relaxation decay in confined liquid systems (such as in vivo bone marrow in trabecular bone, and doped water in glass capillary pipes) are reported and discussed in this paper. Correlated two-dimensional spectroscopy revamped by asymmetricz-gradient echo detection-like sequences were implemented in order to perform intermolecular doublequantum transverse relaxationT _2DQ andT _2DQ ^* measurements. Our experimental results indicated that the relationshipT _2,n ^* =T ₂ ^* /n betweenn-quantum transverse relaxation time and the conventional singlequantumT ₂ ^* only applies for homogeneous systems and fails in the case of highly heterogeneous systems like porous systems.     

Optimized gradient spoiling of UTE VFA-AFI sequences for robust T1 estimation with B1-field correction

Quantifying T₁ relaxation times is a challenge because inhomogeneities of the B₁ field have to be corrected to obtain proper values. It is a particular challenge in tissues with short T₂^⁎ values, for which conventional MRI techniques do not provide sufficient signal. Recently, a B₁-field correction technique called AFI (Actual Flip angle Imaging) has been introduced that can be combined with UTE (ultra-short echo-time) sequences, which have much shorter echo times compared to conventional MRI techniques, allowing quantification of signal in short T₂^⁎ tissues. A disadvantage of AFI is that it requires very long relaxation delays between repetitions to minimize the influence of imperfect spoiling of transverse magnetization on signal behavior. In this work, we propose a novel spoiling scheme for the AFI sequence that efficiently provides accurate B₁ correction maps with strongly reduced acquisition time. We validated the method with both phantom and preliminary in vivo results.