Two coils resonant Ramsey's method for the measurement of time reversal invariance violation in neutron transmission.It is proposed within the framework of Ramsey's method to register two-dimensional spectra, depending on the neutron neutron, uncharged elementary particle of slightly greater mass than the proton. It was discovered by James Chadwick in 1932. The stable isotopes of all elements except hydrogen and helium contain a number of neutrons equal to or greater than the number of protons. phase and neutron energy, for measuring parity (P) and time (T) violating amplitudes of the interaction of polarized A one-way direction of a signal or the molecules within a material pointing in one direction. neutrons with polarized [.sup.139]La nuclei nuclei /nu·clei/ (noo´kle-i) [L.] plural of nucleus. nu·cle·i n. Plural of nucleus. nuclei plural of nucleus. in region of the p-wave resonance. The form of the phase spectrum and corresponding expressions for the asymmetries are obtained on the basis of a formalism Formalism or Russian Formalism Russian school of literary criticism that flourished from 1914 to 1928. Making use of the linguistic theories of Ferdinand de Saussure, Formalists were concerned with what technical devices make a literary text literary, apart of a spin density matrix. It is shown that the ratio of the P,T,-violating to P-violating imaginary amplitudes can be obtained from the measurements of the neutron phase spectrum with polarized and unpolarized [.sup.139]La target. Key words: asymmetries; density matrix; evolution operators; Ramsey's method; scattering amplitude The scattering amplitude describes the amplitude of an outgoing, elementary, spherical wave relative to a plane, incoming wave scattered on a point size particle. Since the spherical wave amplitude varies with  describes charge-parity (CP) violation completely or there are additional sources of CP-violation beyond the framework of SM is an open question. Answers to this question may be found in studies of K, B <a onmouseover=) meson meson (mē`zŏn) [Gr.,=middle (i.e., middleweight)], class of elementary particles whose masses are generally between those of the lepton class of lighter particles and those of the baryon class of heavier particles. decays and also in searches for CP- or T-violation in other areas of physics. As the CP (or T) violating phase of the Cabibbo-Kobayashi-Maskawa (CKM CKM Cabibbo-Kobayashi-Maskawa (quark mixing matrix) CKM Certified Knowledge Manager (trademark of Hudson Associates Consulting, Inc. ) matrix is associated with the sector of heavy quarks Quarks The basic constituent particles of which elementary particles are understood to be composed. Theoretical models built on the quark concept have been very successful in understanding and predicting many phenomena in the physics of elementary particles. , in the field of low energy physics the expected mechanism of T-violation is connected with meson exchange between nucleons [1]. The measured value of the T-violating amplitude in neutron transmission experiments is important in order to improve the value of the isovector pion coupling constant For the Murray-von Neumann coupling constant, see von Neumann algebra. For the coupling constant in NMR spectroscopy, see NMR spectroscopy and/or Proton NMR. In physics, a coupling constant, usually denoted g . The most attractive experiment in this plan is the search for T-violation in a two-level system like [.sup.139]La where in the vicinity of the p-wave resonance, the P-odd effect is enhanced by 5 or 6 orders of magnitude [2]. Similar enhancement is expected for the interaction breaking P-, T-invariance [3]. The problem has been discussed in the literature for more than 20 years, but until now no realistic proposals of such an experiment have been formulated. Traditionally, the scattering amplitude of polarized neutrons with a polarized nucleus is described as follows: f = A + [p.sub.t]B(sI) + C(sk) + [p.sub.t]D(s[kI]). (1) Here I is spin of a nucleus, [p.sub.t] is polarization of a target, s is a neutron spin, and k is its wave vector A wave vector is a vector that specifies the wavenumber and direction of propagation for a wave. The magnitude of the wave vector indicates the wavenumber. The orientation of the wave vector indicates the direction of wave propagation. For example consider a plane wave. . We note that the degree of target polarization can be rather high. So, for example, in Ref. [4] polarization of approximately 50% is obtained with a (15 X 15 X 4) [mm.sup.3] crystal. There are a number of proposals on the determination and measurement of the weak amplitude D [5-11]. The measurement of this amplitude is an asymmetry Asymmetry A lack of equivalence between two things, such as the unequal tax treatment of interest expense and dividend payments. in the counting rate of neutrons polarized with and against the direction of the T-violating field. However, according to according to prep. 1. As stated or indicated by; on the authority of: according to historians. 2. In keeping with: according to instructions. 3. the analysis in Ref. [12, 13], the physical realization of these experiments is extremely difficult. The known theoretical limit [1,2] D [less than or equal to] [10.sup.-4] C, obtained from modern restrictions on the neutron electric dipole moment Noun 1. electric dipole moment - the dipole moment in an electric dipole dipole moment - the moment of a dipole [14], can be reached in proposed experiments. These experiments propose achieving an unprecedented (about [10.sup.-4]) angular accuracy in the orientation of the neutron polarization vector and the requirement that the efficiencies of analyzer and polarizer polarizer an appliance for polarizing light. are equal at the level of [10.sup.-4]. A completely different approach without the specified difficulties and consisting in refusal from the exact orientation of neutron spins concerning a direction of the T-violating field, gives the modified resonant resonant giving an intense, rich sound on percussion; exhibiting resonance. method of oscillating os·cil·late intr.v. os·cil·lat·ed, os·cil·lat·ing, os·cil·lates 1. To swing back and forth with a steady, uninterrupted rhythm. 2. fields. This method allows an increase in the number of degrees of freedom to operate the neutron spectrum. 2. Ramsey's Method The resonant two-coils Ramsey's method [15] is widely applied to measurements of pseudomagnetic fields [16] and updating is reduced to the registration of a phase of a radio-frequency field at the moment of neutron detection Neutron detection is the effective detection of neutrons entering a well-positioned detector. There are two key aspects to effective neutron detection: hardware and software. . Let us define a system of coordinates in which the external magnetic field and the initial polarization vector of the neutrons are directed along the axis z. Neutrons propagate prop·a·gate v. 1. To cause an organism to multiply or breed. 2. To breed offspring. 3. To transmit characteristics from one generation to another. 4. along an axis y and an axis x is the direction of the vector product [k X I]. The amplitude of a radio-frequency field and the length of the coil can be chosen in such a manner that spins of the neutrons having the energy of a p-wave resonance [E.sub.0] = 0.734 eV flip on [[pi]/2], and they are guided in x-y plane perpendicular to an external magnetic field. At random distribution of field phases [delta], which we shall associate with the phase of a neutron, spins with equal probability in a direction are distributed in this plane. The initial density matrix is diagonal and the components of the polarization vector in the chosen system of coordinates are equal: [p.sub.z] = [p.sub.0], = [p.sub.x] = [p.sub.y] = 0. We define as well the geometry of the experimental setup. The length of each coil is equal to l; the length of a target is equal to d; and L is distance between each of coils and a target. Let us select the gyromagnetic ratio Gyromagnetic ratio The ratio of angular momentum to magnetic moment for atomic systems. This ratio is usually expressed in terms of the magnetomechanical factor g′, as in Eq. (1). (1) equal to unity. In this case the neutron spin precession frequency [omega] is equal to the value of magnetic field H. The Hamiltonian for a neutron in the magnetic field is given by: H = [[omega]/2](n[sigma]) = [[omega]/2][[sigma].sub.z]. (2) Here n is the unit vector In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) whose length, (or magnitude) is 1 (the unit length). A unit vector is often written with a superscribed caret or “hat”, like this directed along the magnetic field. For effective fields of a target, we shall accept definitions and designations as in Ref. [12]. The spin dependent part of amplitude in Eq. (1) characterizes the effective field vector b with the following components: a T-violating field [b.sub.x] = [p.sub.t] [D/2], a field of weak interaction [b.sub.y] = [C/2], and a pseudomagnetic field [b.sub.z] = [p.sub.t] [B/2]. ReB represents the residual magnetic field, that is, the difference between the real part of a pseudomagnetic field of a target and an external magnetic field. The target Hamiltonian can then be written as: [H.sub.int] = -i[[lmA]/2]-q([n.sub.1][sigma]). (3) In this expression the spin precession frequency in an effective field is q = [square root of bb] and the unit vector is [n.sub.1] = [b/q]. As is accepted in neutron optics Neutron optics The general class of experiments designed to emphasize the wavelike character of neutrons. Like all elementary particles, neutrons can be made to display wavelike, as well as particlelike, behavior. , the effective fields are complex. Real parts of fields are responsible for a spin precession, and imaginary ones for absorption of neutrons in the substance of a target. The known Hamiltonian defines the corresponding evolution operator U = exp exp abbr. 1. exponent 2. exponential (-iHt), which will transform the density matrix. An expression for the evolution operator in a radio-frequency coil may be found in Ref. [17]: [U.sub.1,2] = exp(-i[[[omega][t.sub.1]]/2])exp(-i[[[[omega].sub.1][t.sub.1]]/2]([n.sub.2][sigma]). Here [t.sub.1] is the neutron flight time through the coil, and the unit vector [n.sub.2] is determined by a phase [delta] of a radio-frequency field at the moment a neutron enters a coil. The components of this vector are given by: [n.sub.2x] = cos[delta], [n.sub.2y] = sin[delta], [n.sub.2z] = 0. 3. A Phase Spectrum of Neutrons and Counting Rate Asymmetries The density matrix of neutrons propagating through the described system is calculated from the following expression: [rho]([delta]) = [U.sub.2][U.sub.L][U.sub.int][U.sub.L][U.sub.1][[rho].sub.0][U.sub.1.sup.+][U.sub.L.sup.+][U.sub.int.sup.+][U.sub.L.sup.+][U.sub.2.sup.+]. (4) Here the indices of evolution operators define, accordingly, the number of the coil, distance L from the coil up to a target, and int--interaction with a target. The two-dimensional neutron spectrum is defined as follows: N = exp(-Im At)Tr([[rho].sub.a][rho]). (5) To define the direction of spin before target, one needs to know the density matrix. It has the following expression: [[rho].sub.L+l] = [U.sub.L][U.sub.1][[rho].sub.0][U.sub.1.sup.+][U.sub.L.sup.+] = [1/2]{1 + [p.sub.0] [[[sigma].sub.x] sin [[omega].sub.1][t.sub.l] cos([delta] + [omega][t.sub.l+L] - [[pi]/2]) + [[sigma].sub.y]sin u [t.sub.1] sin([delta] + [omega][t.sub.l+L] - [[pi]/2]) + [[sigma].sub.z] cos[[omega].sub.1][t.sub.l]]} (6) [t.sub.1+L] is the neutron flight time through the coil, and the interval L up to the target, which is convenient to represent as [t.sub.l+L]. T is the flight time through the entire system. Omitting the exponent exponent, in mathematics, a number, letter, or algebraic expression written above and to the right of another number, letter, or expression called the base. In the expressions x2 and xn, the number 2 and the letter n in Eq. (5), which is responsible for the total loss rate due to absorption in the target and does not merit further interpretation, we obtain an expression for a phase spectrum of neutrons. It follows from Eq. (6) that for the [[pi]/2] coil the interval -[omega][[T - t]/2][less than or equal to][delta][less than or equal to]-[omega][[T - t]/2] + [pi] (7) corresponds to neutrons with the spins distributed in a semi-plane with a positive direction of the x-axis. Phases [delta] shift this interval on [pi] that determines neutrons with spin directions in semi-plane x [??] 0. Shift intervals in Eq. (7) on [[pi]/2] and [3[pi]/2] will set the intervals with spin directions in semi-planes y [??] 0 and y [??] 0, accordingly. Integration of a phase spectrum on the specified intervals gives values [N.sub.+], [N.sub.-], allowing one to calculate the asymmetry in the counting rate of neutrons connected with an axis x (a direction of vector product [k X I]) and an axis y (direction k). [DELTA][N.sub.x] = [N.sub.+x] - [N.sub.-x] = 4sin[[omega].sub.1][t.sub.l] {Im([b'.sub.y][b'*.sub.z])([p.sub.0] + [p.sub.a]cos([epsilon]+[omega]t) + Im([b'.sub.x]cosqt)([p.sub.0] - [p.sub.a]cos([epsilon]+[omega]t)) - [p.sub.a]sin([epsilon] + [omega]t) [Im([b'.sub.x][b'*.sub.z]) + Im([b'*.sub.y] cos qt) + [p.sub.0] cos [[omega].sub.1][t.sub.l](Re([b'.sub.y][b'*.sub.z]) + Re([b'.sub.s]cosqt))] + [p.sub.0][p.sub.a] cos[[omega].sub.1][t.sub.l][Re([b'.sub.x][b'*.sub.z])(1-cos([epsilon] + [omega]t)) - Re([b'.sub.y] cos qt)(1 + cos ([epsilon] + [omega]t))]}, (8) [DELTA][N.sub.y] = [N.sub.+y] - [N.sub.-y] = 4sin [[omega].sub.1][t.sub.l]{Im ([b'.sub.x][b'*.sub.z])([p.sub.0] + [p.sub.a] cos([epsilon] + [omega]t) + Im([b'.sub.y] cos qt)([p.sub.0] - [p.sub.a] cos([epsilon] + [omega]t)) + [p.sub.a] sin([epsilon] + [omega]t) [Im([b'.sub.y][b'*.sub.z]) + Im([b'*.sub.x] cos qt) + [p.sub.0] cos [[omega].sub.1][t.sub.l] (Re([b'.sub.x] [b'*.sub.z]) + Re([b'.sub.y'] cos qt))] + [p.sub.0][p.sub.a] cos [[omega].sub.1][t.sub.l][Re([b'.sub.y] [b'*.sub.z]) (1-cos ([epsilon] + [omega]t)) - Re([b'.sub.x] cos qt)(1+cos([epsilon] + [omega]t))]}. (9) Integration of a phase spectrum in limits from 0 up to 2[pi] gives total number of neutrons: N = [N.sub.+x] + [N.sub.-x] = [N.sub.+y] + [N.sub.-y], N = [1/2]{|[b'.sub.x]|[.sup.2] + |[b'.sub.y]|[.sup.2] + [b'.sub.z]|[.sup.2] + |cos qt|[.sup.2] + [p.sub.0][p.sub.a] [sin.sup.2] [[omega].sub.1][t.sub.l] [(|[b'.sub.z]|[.sup.2] - |cos qt|[.sup.2]) cos ([epsilon] + [omega]t) + 2sin([epsilon] + [omega]t)Re([b'*.sub.z] cos qt)] + [p.sub.0][p.sub.a][cos.sup.2] [[omega].sub.1][t.sub.l](-|[b'.sub.x]|[.sup.2] - |[b'.sub.y]|[.sup.2] + [b'.sub.z]|[.sup.2] + |cos qt|[.sup.2])+2 cos [[omega].sub.1][t.sub.l] [Im([b'.sub.x][b'*.sub.y])([p.sub.0] - [p.sub.a]) + Im([b'*.sub.z] cos qt) ([p.sub.0] + [p.sub.a])]}. (10) The normalization In relational database management, a process that breaks down data into record groups for efficient processing. There are six stages. By the third stage (third normal form), data are identified only by the key field in their record. factors in Eqs. (8-10) are the values n = [N.sub.0] exp (- Im At), where [N.sub.0] is the initial neutron flux Noun 1. neutron flux - the rate of flow of neutrons; the number of neutrons passing through a unit area in unit time flux - the rate of flow of energy or particles across a given surface . 4. Determination of the T-Violating Amplitude Let us discuss the experimental conditions for the determination of a T-violating amplitude. We shall suppose that the degree of compensation of a pseudomagnenic field by external field provides the following inequality |qt| [much less than]1, at which sin(Reqt) [approximately equal to] Reqt and sinh sinh abbr. hyperbolic sine sinh Abbreviation of hyperbolic sine (Imqt) [approximately equal to] Imqt. (11) This condition is satisfied if the residual field equals about 1% of a pseudomagnetic field. For neutrons with the energy at the maximum of p-wave resonance, it is possible to choose the following options of experimental parameters: [MATHEMATICAL EXPRESSION A group of characters or symbols representing a quantity or an operation. See arithmetic expression. NOT REPRODUCIBLE IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ], (12) where [t.sub.0] means time flight for neutron with energy of maximum of p-wave resonance [E.sub.0]. At such parameters, the three last lines in Eqs. (8) and (9) convert in a zero, and it becomes very easy to define the T-violating amplitude in this case. But at a displacement of the neutron energy from [E.sub.0], the suppression factors differ from zero, and one needs to examine backgrounds more carefully. For estimations one uses the fact that in the maximum of the p-wave resonance ReC is close to zero, and ImD [congruent con·gru·ent adj. 1. Corresponding; congruous. 2. Mathematics a. Coinciding exactly when superimposed: congruent triangles. b. to] [10.sup.-4] ImC and in accordance with Eq. (11) ReBt [congruent to] 0.1. Then, in Eq. (8), it is possible to neglect terms in which the values are less than [10.sup.-5] ImCt and in Eq. (9) terms smaller than ImCt by two or more orders of magnitude. As a result of such a reduction, Eqs. (8) and (9) in expanded form give the following expression: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (14) Notice that in Eq. (14) the top signs allow one to define an imaginary part Noun 1. imaginary part - the part of a complex number that has the square root of -1 as a factor imaginary part of a complex number complex number, complex quantity, imaginary, imaginary number - (mathematics) a number of the form a+bi where a and b are real of a P-odd amplitude. We can estimate the contribution of the last term in Eq. (13), considering that in the area of a resonance maximum value, ImC is changed insignificantly. Averaging this term in limits from [t.sub.0] - [DELTA]t up [t.sub.0] + [DELTA]t, we shall obtain [bar.[sin([omega][DELTA]t)ImCt]] = Im C[t.sub.0] [[[omega][t.sub.0]]/3]([[[DELTA]t]/[t.sub.0]])[.sup.2] = Im C[t.sub.0] [[[omega][t.sub.0]]/12]([[DELTA]E]/[E.sub.0])[.sup.2]. In this equality [omega][t.sub.0] is angle of spin turn in a pseudomagnetic field of a target. For 1 cm of La this angle, according to value of the pseudo-magnetic moment from Ref. [16], is 17 radian ra·di·an n. Abbr. rad A unit of angular measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. . The suppression factor in this expression is equal to [10.sup.-6] for the energy window 2 X [10.sup.-3] eV and increases with an increase in the energy interval. It means that the background from ImC can be taken into account if the energy resolution is not worse than between 0.3% and 0.5%. Passing in Eqs. (13) and (14) to average values, we shall obtain a final expression for the determination of the imaginary part of the T-violating field. [[[p.sub.t][bar.ImD]]/[bar.ImC]] = [[bar.[[DELTA][N.sub.x]([pi])]]/[bar.[[DELTA][N.sub.y][pi])]]][1-[[[p.sub.0] - [p.sub.a]]/[[p.sub.0] + [p.sub.a]]][[bar.[[DELTA][N.sub.x](2[pi])]]/[bar.[[DELTA][N.sub.x]([pi])]]]-[[2[p.sub.0]]/[([p.sub.0]+[p.sub.a])[.sup.2]]][[bar.[sin([omega][DELTA]t)[DELTA][N.sub.y]([pi])]]/[bar.[[DELTA][N.sub.x]([pi])]]]]. (15) Because the coefficient in square brackets square bracket n. One of a pair of marks, [ ], used to enclose written or printed material or to indicate a mathematical expression considered in some sense a single quantity. , which depends on the difference in efficiencies of analyzer and polarizer, must be known with precise accuracy, it takes additional measurement for its determination. In the case of a target that is unpolarized and isolated from an external magnetic field, it follows from Eq. (9): [[p.sub.0] - [p.sub.a]]/[[p.sub.0] + [p.sub.a]] = ([[DELTA][N.sub.y](2[pi])]/[[DELTA][N.sub.y]([pi])])[.sub.unpolar]. (16) Equations (15) and (16) represent the essential idea of the method. We suppose exact knowledge of the phase shift between generators of coils and neutron energy. Thus, from this analysis it follows that the measurement of the T-violating amplitude of interaction of the polarized neutrons with the polarized target is reduced to carrying out two experiments with a polarized and non-polarized target. 5. Conclusion Two-dimensional phase spectra of neutrons with energy in the region of the p-wave resonance contain sufficient information for the determination of a T-violating amplitude. The requirements presented here to measure the system in the described method can be realized in feasible experiment. In particular, the precision compensation of a pseudo-magnetic field by an external magnetic field is not obligatory obligatory /ob·lig·a·to·ry/ (ob-lig´ah-tor?e) obligate. obligatory unavoidable; something that is bound to occur. . It is sufficient to have compensation on the level of 1%. One feature of the method is the opportunity of obtaining integrated asymmetries in the neutron counting rate as in the direction of the T-violating field and in the direction of the P-odd field of weak interaction from the same phase spectrum. These two asymmetries define P- and T-violating amplitudes in the maximum of the p-wave resonance. For the determining the amplitude in full region of the resonance, it is necessary to take into account background contributions arising from interaction of neutrons with the pseudo-magnetic field and P-odd field of the weak interaction. In this case the imaginary part of the T-violating field is separated from four neutron spectra, two of which are measured with a non-polarized target. 6. References [1] I. S. Towner and A. C. Hayes, http://arxiv.org/pdf/nucl-th/9402026, April 12, (2004); Phys. Rev. C 49, 2391 (1994); P. Herczeg, Hyperfine Interact. 75, 127 (1992), in Test of Time Reversal Invariance Time reversal invariance A symmetry of the fundamental (microscopic) equations of motion of a system; if it holds, the time reversal of any motion of the system is also a motion of the system. , N. R. Roberson, C. R. Golub, and J. D. Bowman, eds., World Scientific. Singapore (1987) p. 24. [2] V. P. Alfimenkov et al., Nucl. Phys. A 398, 93 (1983); Y. Masuda et al., Nucl. Phys. A 504, 269 (1989). [3] V. E. Bunakov and V P. Gudkov, (Paris) Colloq. 45, C3-77 (1984); JETP JETP Journal of Experimental and Theoretical Physics JETP Jet Propelled Lett. 36, 329 (1982). [4] P. Hautle and M. Iinima, NIM nim 1 tr. & intr.v. nimmed, nim·ming, nims Archaic To steal; pilfer. [Middle English nimen, to take, from Old English niman; see , A 440, 638 (2000). [5] L. Stodolsky, Phys. Lett. B 172, 5 (1986): Nucl. Phys. B 197, 213 (1982). [6] P. K. Kabir, Phys. Rev. D 25, 2013 (1982); Nucl. Inst. Meth. Res. Sect. A 284, 63 (1989). [7] Y. Masuda et al., in Proceedings of WEIN WEIN What Else Is New '92, edited by Ts. D. Vylov, World Scientific, Singapore (1992); Y. Masuda, Los Alamos Los Alamos (lôs ăl`əmōs', lŏs), uninc. town (1990 pop. 11,455), seat of Los Alamos co., N central N.Mex. It is on a long mesa extending from the Jemez Mts. The U.S. Report No. LA-UR-2644. [8] V. Skoy, Phys. Pev. D 53, 4070 (1996). [9] A. P. Serebrov, JETP Lett. 58, 14 (1993). [10] S. I. Pentilla, in Proceedings of ASAP (chat) asap - As soon as possible. 2002, World Scientific (2002) p. 164. [11] T. Masuda, in Proceedings of ASAP 2002, World Scientific (2002), p. 175. [12] S. K. Lamoreaux and R. Golub, Phys. Rev. D 50, 5632 (1994). [13] V. E. Bunakov and I. S. Novikov, Proceedings of the XXXIV Winter School of PNPI PNPI St. Petersburg Nuclear Physics Institute (Russia) , S. Petersburg (2000). [14] K. F. Smith, et al., Phys. Lett., B 234, 191 (1990); I. S. Altarev et al., ibid. 267, 242 (1992); P. G. Harris et al., Phys. Rev. Lett. 82, 904 (1999). [15] N. F. Ramsey, Phys. Rev. 76, 996 (1949). [16] H. Glattli, et al., J. de Phys. 40, 629 (1979). [17] A. Abragam, The Principles of Nuclear magnetism, Clarendon Press, Oxford (1961). V. V. Loukachevitch and A. V. Aldushchenkov St. Petersburg Nuclear Physics Institute RAD (1) (Rapid Application Development) Developing systems incrementally and delivering working pieces every three to four months, rather than waiting until the entire project is programmed before implementing it. , 188350, Gatchina, Leningrad District, Russia lukasche@pnpi.spb.ru aldu@pnpi.spb.ru Accepted: August 11, 2004 Available online: http://www.nist.gov/jres |
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