Cimento Research Articles

Current conservation and analytic determination of the magnetic moment of the Δ resonance in the πN bremsstrahlung: II. Formulation with quark degrees of freedom. III. Magnetic moment of the Δo and Δ− resonances

Our previous paper (Machavariani and Faessler 2010 J. Phys. G: Nucl. Part. Phys. 37 075004) is generalized within the field-theoretical formulation with the quark–gluon degrees of freedom (Huang and Weldon 1975 Phys. Rev. D11 257; Haag 1958 Phys. Rev. 112 669; Nishijima 1958 Phys. Rev. 111 995; Zimmermann 1958 Nuovo Cimento 10 598), where pions and nucleons are treated as the bound (cluster) systems of quarks. It is shown that current conservation for the on-shell πN bremsstrahlung amplitude with the composite nucleons and pions has the same form as in the usual quantum field theory (Itzykson and Zuber 1980 Quantum Field Theory (New York: McGraw-Hill); Bjorken and Drell 1965 Relativistic Quantum Fields (New York: McGraw-Hill)) without quark–gluon degrees of freedom (Machavariani and Faessler 2010). The model-independent representation of the Δ − γ′Δ vertex through the π − γ′π′, N − γ′N′, Δ − πN vertices remain the same in the quantum field theory with the quark–gluon degrees of freedom. Correspondingly, the magnetic dipole moments of the Δ+ and Δ++ resonances in the field-theoretical formulations with and without quark–gluons are identical. These results are extended for the magnetic dipole moments of the Δo and Δ− resonances which are determined via the anomalous magnetic moment of the neutron μn as and .

Editorial on the special issue: Selected papers from the 2nd Joint Italian-Pakistani Workshop on Relativistic Astrophysics

This is a special issue of the journal in which selected papers that were presented in the Second Joint Italian-Pakistani Workshop on Relativistic Astrophysics held in July 2009 at ICRANet, Pescara, Italy are published. This series of Workshops started in June 2007 with a meeting at the University of Salento, Lecce, Italy. It arose from a long time collaboration between the Department of Physics of the Salento University at Lecce, Italy and the Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Islamabad, Pakistan, which was formalized in 2006. The connection between the two Universities had begun due to two of us (FD and AQ) meeting in Rome, where the former was a student of the third (RR) and the latter was a guest of RR. As such, the first Workshop was dedicated to RR. The proceedings were published as a special issue of Nuovo Cimento B, volume 122, number 5, pages 465–616, (officially) in May 2007. The second Workshop was dedicated to John Archibald Wheeler (“Johnny” to his friends and collaborators), who had died on April 13, 2008. The reasons for this

THERMODYNAMIC DETECTION OF QUANTUM PHASE TRANSITIONS

We show that, by recourse to thermodynamics's third law, quantum phase transitions in a system of fermions can be detected, in the sense that thereby one automatically finds the values of the external parameter (here coupling strengths of the pertinent Hamiltonian) at which these transitions occur. We illustrate our considerations with reference to an exactly solvable model of Plastino and Moszkowski [Il Nuovo Cimento 47, 470 (1978)].

An undergraduate exercise in the first law of relativistic thermodynamics

The isothermal compression of an ideal gas is analysed using a relativistic thermodynamics formalism based on the principle of inertia of energy (Einstein's equation) and the asynchronous formulation (Cavalleri and Salgarelli 1969 Nuovo Cimento 42 722–54), which is similar to the formalism developed by van Kampen (1968 Phys. Rev. 173 295–301) and Hamity (1969 Phys. Rev. 187 1745–52). In this 4-vector Minkowski formalism mechanical and thermodynamical processes are described by the first law of thermodynamics expressed as ΔUμ = Wμ + Qμ, in a Lorentz covariant way. This exercise is considered useful for undergraduate physics students interested in foundations of physics, with the only prerequisites in first courses in thermodynamics and special relativity.

Circular Dichroism Tensor of a Triarylmethyl Propeller in Sodium Chlorate Crystals

In 1919, Perucca reported anomalous optical rotatory dispersion from chiral NaClO(3) crystals that were colored by having been grown from a solution containing an equilibrium racemic mixture of a triarylmethane dye (Perucca, E. Nuovo Cimento 1919, 18, 112-154). Perucca's chiroptical observations are apparently consistent with a resolution of the propeller-shaped dye molecules by NaClO(3) crystals. This implies that Perucca achieved the first enantioselective adsorption of a racemic mixture on an inorganic crystal, providing evidence of the resolution of a triarylmethyl propeller compound lacking bulky ortho substituents. Following the earlier report, NaClO(3) crystals dyed with aniline blue are described herein. The rich linear optical properties of (001), (110), and (111) sections of these mixed crystals are described via their absorbance spectra in polarized light as well as images related to linear dichroism, linear birefringence, circular dichroism, and anomalous circular extinction. The linear dichroism fixes the transition electric dipole moments in the aromatic plane with respect to the growth faces of the NaClO(3) cubes. Likewise, circular dichroism measurements of four orientations of aniline blue in NaClO(3) fix a bisignate tensor with respect to the crystal growth faces. Electronic transition moments and circular dichroism tensors were computed ab initio for aniline blue. These calculations, in conjunction with the crystal-optical properties, establish a consistent mixed-crystal model. The nature of the circular extinction depends upon the crystallographic direction along which the crystals are examined. Along 100, the crystals evidence circular dichroism. Along 110, the crystals evidence mainly anomalous circular extinction. These two properties, while measured by the differential transmission of left and right circularly polarized light, are easily distinguished in their transformation properties with respect to reorientations of the sample plates. Circular dichroism is symmetric with respect to the wave vector, whereas anomalous circular extinction is antisymmetric. Analysis of Perucca's raw data reveals that he was observing a convolution of linear and circular optical properties. The relatively large circular dichroism should in principle establish the absolute configuration of the propeller-shaped molecules associated with d- or l-NaClO(3) crystals. However, this determination was not as straightforward as it appeared at the outset. In the solid state, unlike in solution, a strong chiroptical response is not in and of itself evidence of enantiomeric resolution. It is shown how it is possible to have a poor resolution-even an equal population of P and M propellers-within a given chiral NaClO(3) crystal and still have a large circular dichroism.

Thermodynamics’ third law and quantum phase transitions

We report on the fact that microscopically enforcing fulfillment of thermodynamics’ third law on a system of fermions automatically yields the values of the external parameter (here coupling strengths in the pertinent Hamiltonian) at which quantum phase transitions take place. Our considerations are illustrated via an exactly solvable model of Plastino and Moszkowski [Il Nuovo Cimento 47, 470 (1978)].

Indirect study of 11B(p, [formula omitted]) 8Be and 10B(p, α) 7Be reactions at astrophysical energies by means of the Trojan Horse Method: recent results

Nuclear (p, α) reactions destroying the so-called “light-elements” lithium, beryllium and boron have been largely studied in the past mainly because their role in understanding some astrophysical phenomena, i.e. mixing-phenomena occurring in young F-G stars [A.M. Boesgaard et al., Astr. Phys. J, 991, 2005, 621]. Such mechanisms transport the surface material down to the region close to the nuclear destruction zone, where typical temperatures of the order of ∼ 10 6 K are reached. The corresponding Gamow energy E 0 = 1.22 ( Z x 2 Z X 2 T 6 2 ) 1 3 keV [C. Rolfs and W. Rodney, “Cauldrons in the Cosmos”, The Univ. of Chicago press, 1988] is about ∼ 10 keV if one considers the “boron-case” and replaces in the previous formula Z x = 1 , Z X = 5 and T 6 = 5 . Direct measurements of the two 11B(p, α 0 ) 8Be and 10B(p, α) 7Be reactions in correspondence of this energy region are difficult to perform mainly because the combined effects of Coulomb barrier penetrability and electron screening [H.J. Assenbaum, K. Langanke and C. Rolfs, Z. Phys., 327, 1987, 461]. The indirect method of the Trojan Horse (THM) [G. Baur et al., Phys. Lett. B, 178, 1986, 135; G. Calvi et al., Nucl. Phys. A, 621, 1997, 139; C. Spitaleri et al., Phys. Rev. C, 493, 1999, 206] allows one to extract the two-body reaction cross section of interest for astrophysics without the extrapolation-procedures. Due to the THM formalism, the extracted indirect data have to be normalized to the available direct ones at higher energies thus implying that the method is a complementary tool in solving some still open questions for both nuclear and astrophysical issues [S. Cherubini et al., Astr. Phys. J, 457, 1996, 855; C. Spitaleri et al., Phys. Rev. C, 63, 2001, 005801; C. Spitaleri et al., Phys. Rev. C, 63, 2004, 055806; A. Tumino et al., Phys. Rev. Lett., 98, 2007, 252502; M. La Cognata et al., Phys. Rev. Lett., 101, 2007, 152501; M.L. Sergi et al., AIPC, 1016, 2008, 433; H.W. Becker, Z. Phys. A, 327, 1987, 341; T. Rauscher and G. Raimann, Phys. Rev. C, 53, 1996, 5; F.C. Barker, Nucl. Phys. A, 707, 2002, 277; L. Lamia et al., Nuovo Cimento C, 31, 2008, 423; L. Lamia et al., Nucl. Phys. A, 787, 2007, 309c; M.G. Del Santo et al., Proc. of the 10th Symp. on Nuclei in the Cosmos, 2008; C. Angulo et al., Z. Phys. A, 345, 1993, 231].

On the history of the Secchi disc

The first records on regular, tabulated, measurements of transparency of natural waters are those performed by the German naturalist Adelbert von Chamisso during the Russian “Rurik” Expedition 1815–1818 under the command of Otto von Kotzebue. A standardized method to determine the water clarity (transparency) was adopted at the end of the nineteenth century. This method (lowering a white painted disc into the water until it disappeared out of sight) was described by Pietro Angelo Secchi in Il Nuovo Cimento and was published in 1865. The Austrian scientist Josef Roman Lorenz von Liburnau, experimenting with submersible objects, like white discs, in the Gulf of Quarnero (Croatia) in the eighteen-fifties, well before Secchi started his investigations, questioned the naming of the white disc. However, the experiments performed by Secchi and Cialdi in 1864 on such an intensive scale were never performed before. At the beginning of the twentieth century, water transparency observations by means of a 30 cm white disc, was named the Secchi-disc method.

Unsharpness, Naimark Theorem and Informational Equivalence of Quantum Observables

For each commutative POV measure F there exists (Beneduci, J. Math. Phys. 47:062104-1, 2006; Int. J. Geom. Methods Mod. Phys. 3:1559, 2006) a PV measure E such that F can be interpreted as a random diffusion of E. In its turn, the self-adjoint operator A=∫λ dEλ corresponding to E, can be interpreted (Beneduci, J. Math. Phys. 48:022102-1, 2007; Nuovo Cimento B 123:43–62, 2008) as the projection of a Naimark operator corresponding to the Naimark dilation E+ of F. Moreover E can be algorithmically reconstructed by F. All that suggests that, in some sense, the observables represented by E and F should have the same informational content. We introduce an equivalence relation on the set of observables which we compare with other well known equivalence relations and prove that it is the only one for which E is always equivalent to F.

FRW Cosmological Models with Bulk-Viscosity in Barber’s Second Self-Creation Theory

We have studied the evolution of spatially homogeneous and isotropic FRW cosmological model with bulk-viscosity in the frame work of Barber’s (Gen. Relativ. Gravit. 14: 117, 1982) second self-creation theory of gravitation. The cosmological models are obtained with the help of special law of variation for Hubble parameter proposed by Bermann (Nuovo Cimento 74B: 182, 1983). Physical parameters of the models have been discussed in case of false vacuum model, Zel’dovich fluid and radiation dominated fluid.

A Higher Dimensional Cosmological Model in a Scale-Covariant Theory of Gravitation

Kaluza-Klein space-time is considered in the presence of a perfect fluid distribution in the scale-covariant theory of gravitation by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983), a cosmological model in five dimensions with a negative constant deceleration parameter is presented in this theory. Some physical and kinematical properties of the model are also discussed.

Zero mass scalar field with bulk viscous cosmological solutions in Lyra geometry

In this paper, we have investigated spatially homogeneous isotropic Friedmann cosmological model with bulk viscosity and zero-mass scalar field in Lyra manifold. The cosmological models are obtained with the help of the special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) and power law relation. Some physical properties of the models are discussed.

Plane symmetric cosmological models with negative constant deceleration parameter in self creation theory

In this paper, we have investigated plane symmetric cosmological models with negative constant deceleration parameter in Barber’s (Gen. Relativ. Gravit. 14:117, 1982) second self-creation theory in presence of perfect fluid source. For this we use a special law of variation for Hubble parameter proposed by Bermann (Nuovo Cim. B 74:182, 1983) that yields a constant deceleration parameter model of the universe. Some physical properties of the models and entropy are discussed and studied.

A Higher Dimensional Cosmic Domain Wall in Brans-Dicke Theory of Gravitation

Five dimensional Kaluza-Klein Space-time is considered in the presence of thick domain walls in the scalar-tensor theory formulated by Brans and Dicke (Phys. Rev. 124:925, 1961). Exact cosmological model, in this theory, is presented with the help of special law of variation proposed by Berman (Nuovo Cim. B 74:182, 1983) for Hubble’s parameter. Some physical and kinematical properties of the model are also discussed.

Ettore Majorana’s Forgotten Publication on the Thomas-Fermi Model

We analyze the forgotten communication of Ettore Majorana (1906–1938?) on the Thomas-Fermi statistical model of the atom, which he presented on December 29, 1928, during the XXII General Meeting of the Italian Physical Society in Rome, and which was published in Il Nuovo Cimento, the Society’s journal, in 1929. His communication was not mentioned subsequently in any of the numerous publications of Enrico Fermi (1901–1954) and his group in Rome, nor in any of the later accounts of Majorana’s life and work. We place Majorana’s contribution within the context of contemporary research on the subject, point out its influence on the final formulation of the Thomas-Fermi statistical model by Fermi and Edoardo Amaldi (1908–1989) in 1934, and discuss Majorana’s other scientific contributions before his mysterious disappearance in 1938.

The $\bar{\partial}$ -Approach to Monochromatic Inverse Scattering in Three Dimensions

We discuss a method for monochromatic inverse scattering in three dimensions of [Novikov in Int. Math. Res. Papers 2005(6):287–349, [2005]] and implemented numerically in [Alekseenko et al. in Acoust. J. 54(3), [2008]]. This method is obtained as a development of the \(\bar{\partial}\) -approach to inverse scattering at fixed energy in dimension d≥3 of [Beals and Coifman in Proc. Symp. Pure Math. 43:45–70, [1985]] and [Henkin and Novikov in Usp. Mat. Nauk 42(3):93–152, [1987]] and involves, in particular, some results of [Faddeev in Itogi Nauki Tech. Sovr. Prob. Math. 3:93–180, [1965], [1974]] and some ideas of the soliton theory (in particular, some ideas going back to [Manakov in Usp. Mat. Nauk 31(5):245–246, [1976]] and [Dubrovin et al. in Dokl. Akad. Nauk SSSR 229:15–18, [1976]]). Also, our studies go back, in particular, to [Regge in Nuovo Cimento 14:951–976, [1959]]. This article is an extended version of the talk given at International Conference in Mathematics in honor of G. Henkin at the occasion of his 65th birthday.

Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. We performed Monte Carlo simulations to study the phase diagram of such rod-polymer mixture. The colloidal rods were modeled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while the overlap of polymers and rods is forbidden. Large amounts of depletant cause phase separation of the mixture. We estimated the phase boundaries of isotropic-isotropic coexistence both in the bulk and in confinement. To determine the phase boundaries we applied the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)], and we performed a finite size scaling analysis to estimate the location of the critical point. The results are compared with predictions of the free volume theory developed by Lekkerkerker and Stroobants [Nuovo Cimento D 16, 949 (1994)]. We also give estimates for the interfacial tension between the coexisting isotropic phases and analyze its power-law behavior on the approach of the critical point.

Axially symmetric non-static domain walls in scalar–tensor theories of gravitation

An axially symmetric non-static space-time is considered in the presence of thick domain walls in the scalar–tensor theories formulated by Brans and Dicke (Phys. Rev. 124:925, 1961) and Saez and Ballester (Phys. Lett. A 113:467, 1985). Exact cosmological models, in both the theories, are presented with the help of special law of variation proposed by Berman (Nuovo Cim. B 74:182, 1983), for Hubble’s parameter. Some physical and kinematical properties of the models are discussed.

Noncrossing Normal Ordering for Functions of Boson Operators

Normally ordered forms of functions of boson operators are important in many contexts in particular concerning Quantum Field Theory and Quantum Optics. Beginning with the seminal work of Katriel [Lett. Nuovo Cimento, 10(13):565--567, 1974], in the last few years, normally ordered forms have been shown to have a rich combinatorial structure, mainly in virtue of a link with the theory of partitions. In this paper, we attempt to enrich this link. By considering linear representations of noncrossing partitions, we define the notion of noncrossing normal ordering. Given the growing interest in noncrossing partitions, because of their many unexpected connections (like, for example, with free probability), noncrossing normal ordering appears to be an intriguing notion. We explicitly give the noncrossing normally ordered form of the functions (a^{r}(a^{\dag})^{s})^{n}) and (a^{r}+(a^{\dag})^{s})^{n}, plus various special cases. We are able to establish for the first time bijections between noncrossing contractions of these functions, k-ary trees and sets of lattice paths.

Annihilation photon acollinearity in PET: volunteer and phantom FDG studies

Annihilation photon acollinearity is a fundamental but little investigated problem in positron emission tomography (PET). In this paper, the cause of the angular deviation from 180.00° is described as well as how to evaluate it under conditions of a spatially distributed radiation source and a limited acquisition time for the human body. A relationship between the shape of the photopeak spectrum and the angular distribution is formulated using conservation laws of momentum and energy over the pair annihilation. Then the formula is used to evaluate the acollinearity for a pool phantom and the human body with FDG injected. The angular distribution for the pool phantom agrees well with that for pure water which had been directly measured by Colombino et al in 1965 (Nuovo Cimento 38 707–23), and also with that for the human body determined in this study. Pure water can be considered as a good approximation of the human body regarding the angular deviation. The blurring coefficient to be multiplied by the ring diameter in calculations of the PET spatial resolution is experimentally determined for the first time as 0.00243 ± 0.00014; this is 10% larger than the value widely used by investigators.