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The neutron polarimeter SMART-NPOL has been constructed at the RIKEN Accelerator Research Facility for measuring polarization correlations of proton–neutron systems. The SMART-NPOL system consists of 12 parallel neutron counter planes of two dimensionally position-sensitive plastic scintillators with a size of 60 × 60 × 3.0 cm 3 . Polarimetry measurements were made using the analyzing power of the H 1 ( n ⇒ , n ) H 1 reaction occurring in the plastic scintillators. The effective analyzing power of SMART-NPOL was measured with polarized neutrons from the zero-degree Li 6 ( d ⇒ , n ⇒ ) reaction with an incident deuteron energy of 135 MeV / A . The effective analyzing power thus obtained was 0.26 ± 0 . 01 stat ± 0 . 03 syst and the double scattering efficiency was 1.1 × 10 - 3 .

Measurements of deuteron–proton breakup reactions at 135 MeV/A have been made at RIKEN Accelerator Research Facility, focusing on the specific coplanar configurations. The obtained results are compared with the Faddeev calculations based on the modern nucleon–nucleon forces together with the Tucson-Melbourne99, and UrbanaIX three nucleon forces.

The cross sections and spin observables of the pd elastic scattering have been measured at 392 MeV. The results are compared with the prediction of Faddeev calculations with and without including a three nucleon force.

The differential cross sections and the vector analyzing powers for the nd elastic scattering at E n = 250 MeV have been measured for the study of the three-nucleon force (3NF) effects in the Coulomb-free system. To cover a wide angular region, the experiments were performed by using two different methods at the ( n , p ) facility and at the NTOF facility which constructed at the Research Center for Nuclear Physics (RCNP). The results were compared with theoretical predictions of the Faddeev calculations based on the modern nucleon-nucleon (NN) forces with the three-nucleon force (3NF). The inclusion of 3NFs leads to a good description of the cross section except for the backward angles. The results were also compared with the theoretical predictions with relativistic corrections. The direct data-to-data comparison of the cross sections of the nd and pd was performed.

Extensive studies of three-nucleon force (3NF) effects in elastic proton-deuteron scattering have been performed at KVI and elsewhere in the past. In the present work, we explored 3NF effects in the break-up scattering process by performing high precision measurement of vector analyzing powers and differential cross sections using a 190 MeV polarized-proton beam on a liquid deuterium target. The experiment was performed by exploiting a new detector called Big Instrument for Nuclear-polarization Analysis, BINA. Its unique design enables coverage of almost the complete reaction phase space. Preliminary differential cross sections and vector analyzing powers are presented and results are compared with state-of-the-art three-nucleon calculations.

The energy spectrum of the 2 H(d,pn) reaction at 0° at 270 MeV was obtained at RIKEN Accelerator Research Facility. The spectrum in the kinematical region where the resulting pn pair has the relative energy smaller than ∼2 MeV was analyzed by plane-wave impulse approximation calculations assuming the configurations of final state interaction with s-wave.

The 116Cd(p,n) experiment at 300 MeV has been performed for deducing the Gamow-Teller (GT) transition strengths B(GT−) in 116In. For the transition to the ground state, the B(GT−) value of 0.26 ± 0.02 is obtained. From this B(GT−) value and the B(GT+) value by a beta-decay experiment, the contribution of the intermediate ground state of 116In to the nuclear matrix element is deduced to be 0.070 ± 0.003. The B(GT−) value obtained herein is a factor of 8 less than that obtained from a previous (3He,t) measurement. This discrepancy, as well as differences in the distribution of low energy GT strength, and the width and peak energy of the GT giant resonance may be explained if the target used in the (3He,t) measurement is a Cd target with natural abundance.

High-precision vector and tensor analyzing powers of elastic deuteron-proton (d + p) scattering have been measured at intermediate energies to investigate effects of three-nucleon forces. Angular distributions in the range of 70-120 degrees in the center-of mass frame for incident-deuteron energies Ed (lab)(d) = 130 and 180 MeV were obtained using the RIKEN facility. The beam polarization was unambiguously determined by measuring the C-12(d,alpha)B-10(2(+)) reaction at 0 degrees. Results of the measurements are compared with state-of-the-art three-nucleon calculations. The present modeling of nucleon-nucleon forces and its extension to the three-nucleon system is not sufficient to describe the high-precision data consistently and requires, therefore; further investigation.

We report measurements of the cross section and a complete set of polarization observables for the Si 28 ( p → , n → ) P 28 ( 6 − ) reaction at a bombarding energy of 198 MeV. The data are compared with distorted wave impulse approximation calculations employing response functions normalized to inelastic electron scattering. The spin-longitudinal polarized cross section I D q is slightly over-predicted by the calculations, while the normal spin-transverse polarized cross section I D n is significantly under-predicted. The calculated in-plane spin-transverse I D p and spin-scalar I D 0 polarized cross sections agree well with the experimental data. These results are consistent with those for Si 28 ( p → , p → ′ ) Si 28 ( 6 − , T = 1 ) scattering at the same energy, and thus it is concluded that isospin-mixing effects are not responsible for the discrepancy between theory and experiment in the ( p → , p → ′ ) case. Energy half-off-shell effects as medium effects on the effective nucleon–nucleon interaction are also investigated and found to be too small to be responsible for the discrepancy.

Heavy-ion beam charge stripping at 2.7 MeV/u is studied, experimentally and theoretically, for different low-Z gas stripper targets.

We have constructed a new type of spin polarized solid proton target which can be operated under a low magnetic field of 0.08T and a high temperature of 100 K. We have measured for the first time the polarization asymmetry of an unstable beam of 6He at an energy of 71 MeV/u. Optical potential analyses have been carried out.

A new type of the spin polarized solid proton target has been constructed which can be operated under a low magnetic field of 0.08 T and a high temperature of 100 K. First polarization asymmetry measurement with an unstable beam of 6He with an energy of 71 MeV/u has been successfully carried out.

To study the three-nucleon force (3NF) effects without ambiguities from the Coulomb effect, the differential cross sections and the vector analyzing powers for the [Formula: see text] elastic scattering at En = 245 MeV have been measured at θcm = 85° - 180°. The data are compared to the results of Faddeev calculations using modern nucleon-nucleon (NN) forces with and without 3NF. Additionally we have a plan to extend our measurement to the forward angular region where the Coulomb effect is expected to be large. We carried out the test experiment and measured the differential cross sections at θcm = 21°.

The cross sections and spin observables of the p+d elastic scattering have been measured at 392 MeV. The results are compared with the results of Faddeev calculations with and without including the three nucleon force.

Vector analyzing powers for proton elastic scattering from 8He at 71 MeV/nucleon have been measured using a solid polarized proton target operated in a low magnetic field of 0.1 T. The spin-orbit potential obtained from a phenomenological optical model analysis is found to be significantly shallower and more diffuse than the global systematics of stable nuclei, which is an indication that the spin-orbit potential is modified for scattering involving neutron-rich nuclei. A close similarity between the matter radius and the root-mean-square radius of the spin-orbit potential is also identified., Comment: 6 pages, 4 figures, accepted for publication in Physical Review C Rapid Communication

Development of a nondestructive, efficient electric-charge-stripping method is a key requirement for next-generation high-intensity heavy-ion accelerators such as the RIKEN Radioactive-Isotope Beam Factory. A charge stripper employing a low-$Z$ gas is an important candidate applicable to high-intensity uranium beams for replacing carbon-foil strippers. In this study, a high-beam-transmission charge-stripping system employing helium gas for $^{238}\mathrm{U}$ beams injected at $10.8\text{ }\text{ }\mathrm{MeV}/\mathrm{u}$ was developed and demonstrated for the first time. The charge-state evolution measured using helium in a thickness range of $0.24--1.83\text{ }\text{ }\mathrm{mg}/{\mathrm{cm}}^{2}$ is compared with theoretical predictions. Energy attenuation and energy spread due to the helium stripper are also investigated.

The double-differential cross sections for the ${}^{116}$Cd$(p,\phantom{\rule{-0.16em}{0ex}}n)$ and ${}^{116}$Sn$(n,\phantom{\rule{-0.16em}{0ex}}p)$ reactions were measured at 300 MeV for studying the nuclear matrix element of the ${}^{116}$Cd $\ensuremath{\beta}\ensuremath{\beta}$ decay. A multipole decomposition technique was applied to the spectra to extract the Gamow-Teller (GT) component. The integrated GT strengths up to an excitation energy of 30 MeV in the intermediate nucleus ${}^{116}$In are $40\ifmmode\pm\else\textpm\fi{}6$ and $11\ifmmode\pm\else\textpm\fi{}1$ in the $(p,\phantom{\rule{-0.16em}{0ex}}n)$ and $(n,\phantom{\rule{-0.16em}{0ex}}p)$ spectra, respectively, including the component from the isovector spin monopole (IVSM). The spectra are compared with those obtained from a theoretical calculation with a quasiparticle random phase approximation, where the contribution from the IVSM component as well as the interference effect between the GT and IVSM components are fully taken into account.

The vector analyzing power has been measured for the elastic scattering of neutron-rich 6He from polarized protons at 71 MeV/nucleon making use of a newly constructed solid polarized proton target operated in a low magnetic field and at high temperature. Two approaches based on local one-body potentials were applied to investigate the spin-orbit interaction between a proton and a 6He nucleus. An optical model analysis revealed that the spin-orbit potential for 6He is characterized by a shallow and long-ranged shape compared with the global systematics of stable nuclei. A semimicroscopic analysis with a alpha+n+n cluster folding model suggests that the interaction between a proton and the alpha core is essentially important in describing the p+6He elastic scattering. The data are also compared with fully microscopic analyses using non-local optical potentials based on nucleon-nucleon g-matrices., 20 pages, 20 figures, accepted by Physical Review C

The charge-state distributions of U with energies of 14 and 15 MeV=nucleon were measured using nitrogen (N2) gas and carbon foil (C-foil) charge strippers. The most probable charge states of U with energies of 14 and 15 MeV=nucleon in N2 gas attain equilibrium at 60.8 and 62.4, whereas those in C-foils attain equilibrium at 75.8 and 76.7, respectively. Novel empirical formulas for the accurate prediction of the equilibrium charge states of U with energies 10–20 MeV=nucleon in gases and C-foil were derived by fitting the data in the energy range of 1–20 MeV=nucleon. The charge states predicted by using the formulas for gases and C-foil are in good agreement with the data in the energy range of 10–20 MeV=nucleon within an average of 0.23 and 0.21, respectively.

The RIKEN accelerator complex started feeding the next-generation exotic beam facility radioisotope beam factory (RIBF) with heavy-ion beams from 2007 after the successful commissioning of RIBF at the end of 2006. Many improvements made from 2007 to 2010 were instrumental in increasing the intensity of various heavy-ion beams. However, the available beam intensity of very heavy ion beams, especially uranium beams, is far below our goal of $1\text{ }\text{ }\mathrm{p}\ensuremath{\mu}\mathrm{A}$ ($6\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }\text{ }\mathrm{particles}/\mathrm{s}$). In order to achieve this goal, upgrade programs are already in progress; the programs include the construction of a new 28-GHz superconducting electron cyclotron resonance ion source and a new injector linac. However, the most serious problem, that of a charge stripper for high-power uranium beams, still remains unsolved, despite extensive research and development work using large foils mounted on a rotating cylinder and a ${\mathrm{N}}_{2}$ gas stripper. A gas stripper is free from problems related to lifetime, though the equilibrium charge state in this stripper is considerably lower than that in a carbon foil, owing to the absence of the density effect. Nevertheless, the merits of gas strippers motivated us to develop a low-$Z$ gas stripper to achieve a higher equilibrium charge state even in gases. We measured the electron-loss and electron-capture cross sections of uranium ions in He gas as a function of their charge state at 11, 14, and $15\text{ }\text{ }\mathrm{MeV}/\mathrm{nucleon}$. The equilibrium charge states extracted from the intersection of the lines of the two cross sections were promisingly higher than those in ${\mathrm{N}}_{2}$ gas by more than 10. Simple simulations of charge development along the stripper thickness were performed by assuming the measured cross sections. The simulation results show that about $1\text{ }\text{ }\mathrm{mg}/{\mathrm{cm}}^{2}$ of He gas should be accumulated to achieve a charge state higher than that of ${\mathrm{N}}_{2}$ gas, notwithstanding the difficulty in accumulation of this helium amount owing to its fast dispersion. However, we now believe that the following two solutions can overcome this difficulty: a gas cell with a very large differential pumping system and a gas cell with a plasma window. Their merits and demerits are discussed in the paper.

The charge-state distributions and equilibrium charge states of uranium ($^{238}\mathrm{U}$) and xenon ($^{136}\mathrm{Xe}$) ions at $11\text{ }\text{ }\mathrm{MeV}/\mathrm{nucleon}$ were determined using a gas charge stripper. A differential pumping system facilitated the increase of the nitrogen gas thickness up to $1.3\text{ }\text{ }\mathrm{mg}/{\mathrm{cm}}^{2}$, which is sufficient for the most probable charge state to attain equilibrium. The charge states of $^{238}\mathrm{U}$ attain equilibrium at 56.0, 56.6, and 55.7 in ${\mathrm{N}}_{2}$, Ar, and ${\mathrm{CO}}_{2}$ media with thicknesses of 125, 79, and $126\text{ }\text{ }\ensuremath{\mu}\mathrm{g}/{\mathrm{cm}}^{2}$, respectively, while those of $^{136}\mathrm{Xe}$ attain equilibrium at 40.5, 40.1, and 40.3 in ${\mathrm{N}}_{2}$, Ar, and ${\mathrm{CO}}_{2}$ media with thicknesses of 163, 95, and $139\text{ }\text{ }\ensuremath{\mu}\mathrm{g}/{\mathrm{cm}}^{2}$, respectively. The equilibrium charge states of $^{136}\mathrm{Xe}$ are acceptable for acceleration by the subsequent cyclotron. The measured data of $^{238}\mathrm{U}$ were used to devise an empirical formula for the prediction of the equilibrium charge state in gaseous media over the energy region of $0.01--60\text{ }\text{ }\mathrm{MeV}/\mathrm{nucleon}$. The equilibrium charge state of $^{136}\mathrm{Xe}$ as predicted by the devised formula is in good agreement with the data.

Vector analyzing power for the proton-{sup 6}He elastic scattering at 71 MeV/nucleon has been measured for the first time, with a newly developed polarized proton solid target, which works at a low magnetic field of 0.09 T. The results are found to be incompatible with a t-matrix folding model prediction. Comparisons of the data with g-matrix folding analyses clearly show that the vector analyzing power is sensitive to the nuclear structure model used in the reaction analysis. The {alpha}-core distribution in {sup 6}He is suggested to be a possible key for understanding the nuclear structure sensitivity.

Precision data are presented for the break-up reaction, $^2{\rm H}(\vec p,pp)n$, within the framework of nuclear-force studies. The experiment was carried out at KVI using a polarized-proton beam of 190 MeV impinging on a liquid-deuterium target and by exploiting the detector, BINA. Some of the vector-analyzing powers are presented and compared with state-of-the-art Faddeev calculations including three-nucleon forces effect. Significant discrepancies between the data and theoretical predictions were observed for kinematical configurations which correspond to the $^2{\rm H}(\vec p,^2$He$)n$ channel. These results are compared to the $^2{\rm H}(\vec p,d)p$ reaction to test the isospin sensitivity of the present three-nucleon force models. The current modeling of two and three-nucleon forces is not sufficient to describe consistently polarization data for both isospin states., 4 pages, 3 figures, submitted to PRL

The double-differential cross sections for the 48Ca(p,n) and 48Ti(n,p) reactions were measured at 300 MeV. A multipole decomposition technique was applied to the spectra to extract the Gamow-Teller (GT) components. The integrated GT strengths up to an excitation energy of 30 MeV in 48Sc are 15.3+/-2.2 and 2.8+/-0.3 in the (p,n) and (n,p) spectra, respectively. In the (n,p) spectra additional GT strengths were found above 8 MeV where shell models within the fp shell-model space predict almost no GT strengths, suggesting that the present shell-model description of the nuclear matrix element of the two-neutrino double-beta decay is incomplete.

The deuteron to proton polarization transfer coefficients ${K}_{\mathit{yy}}^{{y}^{'}}$ and ${K}_{y}^{{y}^{'}}$ together with the deuteron analyzing powers are measured in three coplanar configurations of the deuteron-proton breakup reaction with a 135-MeV/nucleon polarized deuteron beam at the RIKEN Accelerator Research Facility. The data are compared with theoretical predictions based on exact solutions of the three-nucleon ($3N$) Faddeev equations with high-precision nucleon-nucleon ($\mathit{NN}$) forces, alone or combined with two $3N$ force (3NF) models, the $2\ensuremath{\pi}$-exchange Tucson-Melbourne${}^{'}(99)$ (${\mathrm{TM}}^{'}99$) and Urbana IX. Large 3NF effects have been found for all the measured observables. Predicted effects are supported by the data, with the exception of the vector analyzing power ${A}_{y}^{d}$. For this observable, theory based on only $\mathit{NN}$ forces is sufficient to explain the data. The behavior of the breakup analyzing powers is found to be different from the corresponding observables in elastic nucleon-deuteron scattering.

The double-differential cross sections for the 48Ca(p,n) and 48Ti(n,p) reactions were measured at 300 MeV. A multipole decomposition technique was applied to the spectra to extract the Gamow-Teller (GT) components. The integrated GT strengths up to an excitation energy of 30 MeV in 48Sc are 15.3+/-2.2 and 2.8+/-0.3 in the (p,n) and (n,p) spectra, respectively. In the (n,p) spectra additional GT strengths were found above 8 MeV where shell models within the fp shell-model space predict almost no GT strengths, suggesting that the present shell-model description of the nuclear matrix element of the two-neutrino double-beta decay is incomplete.

Gamow-Teller (GT) unit cross sections, ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{\mathrm{GT}}$, are obtained at 198 and 297 MeV by measuring the double differential cross sections at ${0}^{\ifmmode^\circ\else\textdegree\fi{}}$ for the $(p,n)$ reaction on $^{58}\mathrm{Ni}$, $^{70}\mathrm{Zn}$, $^{114}\mathrm{Cd}$, $^{118}\mathrm{Sn}$, and $^{120}\mathrm{Sn}$. The mass dependence of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{\mathrm{GT}}$ and the ratio of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{\mathrm{GT}}$ to the Fermi unit cross section, ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{\mathrm{F}}$, $({R}^{2})$ are also derived in the mass region of $58\ensuremath{\leqslant}A\ensuremath{\leqslant}120$. The ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{\mathrm{GT}}$ value for $^{90}\mathrm{Zr}$ at 297 MeV interpolated using the $A$-dependence obtained herein agrees with that used in a previous analysis where the GT transition strength over a wide energy region up to the continuum was discussed. However, the deduced $^{64}\mathrm{Ni}$${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{\mathrm{GT}}$ value at 198 MeV is 20% smaller than that obtained from the analysis of a previous $(n,p)$ measurement. The present ${R}^{2}$ values in the mass region heavier than $^{42}\mathrm{Ca}$ are larger than those in the region up to $^{42}\mathrm{Ca}$ and increase as a function of $A$.

The double differential cross sections for the 116Cd(p,n) and 116Sn(n,p) reactions at 300 MeV have been measured over a wide excitation‐energy region including Gamow‐Teller (GT) giant resonance (GTGR) for studying GT transition strengths in the intermediate nucleus of the 116Cd double‐β decay, namely 116In. A large amount of the strengths in the β+ direction has been newly found in the energy region up to 30 MeV, which may imply that the GT strengths in the GTGR region contribute to the nuclear matrix element of the two‐neutrino double‐β decay.

Type II binomial distribution of order k was introduced by Ling (1988). In this article the probability function, the probability generating function and asymptotic properties of the distribution are discussed. Some properties of the corresponding negative binomial distribution of order k , which was introduced by Ling (1989) are also examined.

A systematic study of three-nucleon force (3NF) effects in break-up reactions has been carried out at KVI at several energies. In this article, the p + d -> p + p + n reaction with a polarized-proton beam of 190 MeV will be discussed. The experiment was performed by exploiting a new detector called BINA. Some results for high-precision vector analyzing powers and differential cross sections are presented and compared with state-of-the-art Faddeev calculations with or without 3NF.

The differential cross sections and vector analyzing powers for $\mathit{nd}$ elastic scattering at ${E}_{n}=248$ MeV were measured for $10\ifmmode^\circ\else\textdegree\fi{}--180\ifmmode^\circ\else\textdegree\fi{}$ in the center-of-mass (c.m.) system. To cover the wide angular range, the experiments were performed separately by using two different setups for forward and backward angles. The data are compared with theoretical results based on Faddeev calculations with realistic nucleon-nucleon ($\mathit{NN}$) forces such as AV18, CD Bonn, and Nijmegen I and II, and their combinations with the three-nucleon forces (3NFs), such as Tucson-Melbourne 99 (TM99), Urbana IX, and the coupled-channel potential with \ensuremath{\Delta}-isobar excitation. Large discrepancies are found between the experimental cross sections and theory with only $2N$ forces for ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}g90\ifmmode^\circ\else\textdegree\fi{}$. The inclusion of 3NFs brings the theoretical cross sections closer to the data but only partially explains this discrepancy. For the analyzing power, no significant improvement is found when 3NFs are included. Relativistic corrections are shown to be small for both the cross sections and the analyzing powers at this energy. For the cross sections, these effects are mostly seen in the very backward angles. Compared with the $\mathit{pd}$ cross section data, quite significant differences are observed at all scattering angles that cannot be explained only by the Coulomb interaction, which is usually significant at small angles.

A proton polarimeter EPOL has been constructed at the focal plane of the spectrograph SMART at RIKEN. EPOL is designed for the test of EPR paradox in a two proton system by measuring the spin-correlation of the ' H ( d , p p [ ' S o ] ) n reaction at E d = 270 MeV. EPOL consists of a spin-analyzer target (graphite slab), plastic scintillation counter hodoscopes and multi-wire drift chambers. EPOL is capable of identifying the trajectories of two protons before and after scattering in the analyzer target. EPOL has been calibrated at Ep = 12&160 MeV. The effective analyzing power is 0.17-0.23 and the figure of merit is 0.7-2.6 x lop3, both of which increase with incident energy.

Vector analyzing power was measured for the proton elastic scattering on 6He at 71 MeV/u. We applied a solid polarized proton target, which was operated in a low magnetic field of 88 mT and at high temperature of 100 K, to a radioactive‐isotope beam experiment. Low energy recoil protons were successfully detected due to the modest operation conditions of the target. Selection of p+6He elastic scattering events was clearly carried out with detected protons. Absolute values of the analyzing power were determined for the first time.

We report the results of the first-time test of the local hidden variable theories (Bell-Clauser-Horne-Shimony-Holt) involving strongly interacting pairs of massive spin 1/2 hadrons from the decay of short-lived (tau10;-21sec) 2He spin-singlet state, populated in the nuclear reaction 2H+;1H--;2He+n. The novel features of this experiment are (a) the use of an 'event-ready' [corrected] detector of nearly 100% efficiency to prepare an unbiased sample and (b) a focal-plane polarimeter of full 2pi sr acceptance with a random "post selection" of the reference axes. The spin-correlation function is deduced to be S[exp](pi/4)=2.83+/-0.24stat+/-0.07sys. This result is in agreement with nonlocal quantum mechanical prediction and it violates the Bell-CHSH inequality of |S|or=2 at a confidence level of 99.3%.

Supernarrow dibaryons (SNDs) have been searched for by the $\mathit{pd}\ensuremath{\rightarrow}\mathit{ppX}$ and $\mathit{pd}\ensuremath{\rightarrow}\mathit{pdX}$ reactions at ${E}_{p}=295$ MeV over a mass range of 1898 to 1953 MeV, where three candidates of SNDs were found at the Moscow Meson Factory. The experiment was carried out at the Research Center for Nuclear Physics using a two-arm magnetic spectrometer system and a liquid deuterium target. A good mass resolution of 1 MeV and a low background condition were achieved. No resonance structure was observed in the missing mass spectra. Upper limits of the SND production cross section were determined.