Determination of the flux of primary cosmic ray hydrogen and helium nuclei near the geomagnetic equator using nuclear emulsions

The flux of helium nuclei of the primary cosmic radiation at the top of the atmosphere has been determined over Hyderabad, India, at a time of high solar activity in the 11-year cycle, namely March 24, 1960. The flux value has been found to be 17·9±1·9 helium nuclei per m.² sec. ster. corresponding to a vertical geomagnetic cut off energy of 7·5 GeV/nucleon. This result when compared with other observations made near the geomagnetic equator shows that the solar modulation effects, if any, at rigidities >16 GV should be ?10% only.     

He3 nuclei in the low energy primary cosmic radiation

The flux of He³ nuclei and the ratio He³/(He³+He⁴) in the low energy primary cosmic radiation have been determined using a stack of nuclear emulsions exposed at 3·1 g. cm.^?2 of atmospheric depth from Fort Churchill, Canada, in June 1963. The grain-densityversus residual range method was used to determine the masses of the helium nuclei. Using a sample of 146 helium nuclei whose masses could be identified, the ratio He³/(He³+He⁴) is obtained as 0·14±0·04 for the kinetic energy interval 115–210 MeV per nucleon and 0·43±0·11 for the rigidity interval 0·85–1·05 BV. The differential fluxes of He³ nuclei are determined as 0·017±0·006, 0·045±0·015, and 0·054±0·017 particles/M². Sr. Sec. MeV/nucleon, in the kinetic energy intervals of 117–183, 183–217, and 217–250 MeV/nucleon respectively. These results are compared with those of other investigators. From the results of the present work the amount of matter traversed in space by the primary cosmic ray helium nuclei of energy 115–210 MeV/nucleon is obtained as 4·7±1·8 gm. cm.^?2 of hydrogen.     

Recent observations on cosmic electrons and their consequences on different cosmic ray models and related astrophysical quantities

An experiment has been carried out to study the electron component of the primary cosmic radiation at energies >12 GeV using a hypersensitised nuclear emulsion stack, flown oriented in the east-west plane over Hyderabad, India. The results of this experiment, on the basis of 28 identified electrons of energy above 12 GeV are: (i) the integral flux of electrons above an effective energy of 16 GeV is 0·51±·10 per m.² sec. sr.; (ii) the differential energy spectrum between 12 and 300 GeV can be represented as N(E)dE=12·7 E^?2.1±·2 dE m.^?2 sec.^?1 sr.^?1; and (iii) the fraction of positrons among the total electrons in the energy region 12 to 30 GeV has been discussed. A critical study has been made on the applicability of different cosmic ray models by making use of the observed differential energy spectrum of electrons and the relevant astrophysical parameters associated with the confinement regions. The confinement regions considered are: (i) the universe as a whole, (ii) the super cluster to which our galaxy belongs, (iii) the galactic halo and (iv) the galactic disc. The consequences of the recently postulated universal black body radiation at 3° K. on the cosmic ray models have also been considered. Some of the crucial experiments needed to set more stringent constrains on the models which would then permit meaningful interpretation, are enumerated.     

Determination of the flux of primary cosmic ray hydrogen and helium nuclei near the geomagnetic equator using nuclear emulsions

Nuclear emulsions exposed to the cosmic radiation over Hyderabad, India, at an altitude of 31·3 km. for six hours, have been used to derermine primary cosmic ray deuteron flux. The flux of deuterons of rigidity ?16·9 GV at the top of the atmosphere is found to be <10 m.^?2 sec.^?1 sterad^?1; this may be compared with the proton fiux of 83±12 m.^?2 sec.^?1 sterad.^?1 in the same rigidity region over Hyderabad.     

Investigations on multiply charged nuclei of the primary cosmic radiation near the geomagnetic equator using nuclear emulsions

The charge spectrum obtained from measurements made on tracks of 1329 nuclei of the cosmic radiation of Z?6 and E?7·5 GeV/n has been studied in detail using emulsion stacks exposed over Hyderabad, India (cut off rigidity=16·8 GV) at a depth of 6·8 g/cm² of air for 7¼ hrs. This spectrum has been compared with that available for nuclei of E≥1·5 GeV/n. Within the limits of experimental errors, no dependence of the flux values or ratios of intensities with energy are noticed. This result has important implications on the origin and history of the cosmic radiation. Integral energy spectra of M and H-nuclei have been derived making use of the flux values at the two locations; the spectra thus derived have the least errors associated with these.     

Investigations on the multiply charged nuclei of the primary cosmic radiation near the geomagnetic equator using nuclear emulsion

A nuclear emulsion stack was exposed over Hyderabad, India (geomagnetic latitudeλ=7·6° N) under a mean atmospheric depth of 6·8 g./cm.², on 24 March 1960. The relative and absolute intensities of Be and B nuclei and nuclei of charge Z?6 (the S-nuclei) have been determined in this stack. The intensities were extrapolated to the top of the atmosphere using measured fragmentation parameters involved in collisions of cosmic ray nuclei in graphite. The flux values of Be, B and S nuclei at the top of the atmosphere have been determined to be 0·025±0·011, 0·101±0·023 and 1·12±0·10 particles/m.² sec. sr. respectively. The ratios of intensities B/S, Be/S and Be/B have been found to be 0·09±0·02, 0·022±0·008 and 0·25±0·11 respectively. These ratios of intensities have been used (a) to compute the amount of matter traversed by the radiation before reaching the vicinity of the earth as 2·6±0·6 g./cm.², (b) to show that the Fermi mechanism of acceleration of particles is not efficient at these energies (1–10 GeV/n.) in interstellar space and (c) to show that preferential acceleration of H₁-nuclei (Z?20) is not of overwhelming importance. The derived source composition of nuclei of energy ?7·5 GeV/n suggests that N, O, F and H₃-nuclei (Z=10–15) have similar abundances in the universe and in cosmic rays, and that C and H₁-nuclei are overabundant in cosmic rays.     

Nuclear disintegrations produced in nuclear emulsions by α-particles of great energy

A study of nuclear disintegrations caused by α-particles of primary cosmic radiation with energies > 5 BeV per nucleon, has been carried out. In a systematic survey in nuclear emulsions using ‘along the track’ scanning method, 479 α-particles with a total track length of 40·84 metres and 242 interactions were obtained. From the angular distribution of shower particles associated with these interactions, a procedure has been found for distinguishing protons, which originally formed part of the incident α-particle and which have not taken part in the interaction, from other charged particles. The mean free path for nuclear interaction in G-5 emulsion is found to be 17·5±1·1 cm. (68·9±4·3 gm./cm.²). Assigning both to the incident α-particle and to the target nuclei a radius R=r _oA^1/2, one obtains an effective nuclear radiusr _o=1·13±0·04 ×10^?13 cm. Using the number of protons emerging from disintegrations of heavy nuclei (Silver and Bromine) without having participated in the interaction (as can be deduced from the angular distribution) and assuming spherical nuclei of uniform density, the mean free path of nucleons in nuclear matter is calculated to be less than 3·2×10^?13 cm.     

Directional variation of geomagnetic cut-off rigidity around Hyderabad,India

The geomagnetic cut-off rigidities for cosmic ray particles arriving at the top of the atmosphere over Hyderabad, India (geographic latitude 17.6°N. and longitude 78.5° E.), as a function of zenith and azimuthal angles and the vertical cut-off rigidities for a few neighbouring locations, have been made using the sixth degree simulation of the geomagnetic field by the C.D.C. 3600 Computer.     

Cosmic ray nuclei of chargeZ⩾3 during the period of low solar activity

A detailed study of the composition and energy spectra of heavy nuclei of charge Z?3 in the primary cosmic rays has been made during the period of low solar activity, using two stacks of nuclear emulsions exposed in balloon flights from Fort Churchill, Canada, in June 1963. Each of the stacks was composed of 120 nuclear emulsions of three different sensitivities and was exposed at about 3·5 g. cm.^?2 of residual air for about 11.1 hr. Reliable resolution of charges of nuclei from lithium to oxygen was obtained; for heavier nuclei, charge groups were determined. From the analysis of 793 tracks of nuclei with Z?3, results on the following aspects were obtained:

1. The differential energy spectra of L (Z=3–5), M (Z=6–9) and H (Z=10–28) nuclei were measured in the energy intervel 150–600 MeV/nucleon; integral fluxes were obtained for energy >600 MeV/nucleon;
2. The energy dependence of the L/M ratio at the top of the atmosphere was determined; the ratios were obtained as 0·45 ± 0·06 and 0·29 ± 0·03 in the energy intervals of 200–575, and >575 MeV/nucleon respectively;
3. Relative abundances of individual nuclei of Li, Be, B, C, N and O at the top of the atmosphere were determined as 36, 29, 55, 100, 60 and 106 respectively in the energy interval 150–600 MeV/nucleon; corresponding values were also obtained for energy >600 MeV/nucleon.
4. The differential fluxes of multiply charged nuclei measured by us and by other investigators were used to determine the solar modulation between solar maximum to solar minimum. It was found that solar modulation of the fluxes of M and He nuclei were consistent with Rβ dependence and that the modulation parameter Δη between 1965 and 1957 was about 1·1.

The implications of these results are discussed.     

A possible cosmic ray primary particle energy spectrum above 104 GeV and its astrophysical implications

A primary cosmic ray particle energy specturm of Galactic origin with a sharp cut-off at an energy per nucleon of 3 × 10⁴ GeV for protons and 5 × 10⁴ GeV for heavier particles and extending only upto energies ～ 10¹⁵ eV is deduced in part from the observed cosmic ray phenomena at the highest energies. It appears that the cut off is not due to the magnetic rigidity of the particles in the Galaxy but due to a cut off in or near the sources themselves. In particular, it is pointed out that Fermi type of acceleration is unlikely to be important in the production of energetic cosmic ray particles in the Galaxy. A pedestal in the energy spectrum from an extra Galactic component upto a maximum energy per nucleon ～ 10⁷ GeV with an upper limit of total energies ～ 10¹⁸ eV has been added.     

Investigations on the multiply charged nuclei of the primary cosmic radiation near the geomagnetic equator using nuclear emulsions

The interaction mean-free paths and fragmentation parameters associated with collisions of nuclei of Z?6 and E?7·5 Gev/n have been measured using emulsion-graphite sandwich stacks exposed to the primary cosmic radiation at Hyderabad, India (Geomagnetic latitudeλ=7·6° N). The results are based on a total of 213 nuclear interactions observed in graphite. Since the atomic number of graphite is very close to the mean atomic number of air, the parameters derived for graphite medium are directly applicable to air. A comparative study has been made of the results thus obtained with similar data available for nuclei of E?1·5 Gev/n.     

Thermal expansion of ferroelectrics

Using the interference method the thermal expansion of lithium hydrazinium sulphate [Li(N₂H₅)SO₄] has been investigated in the temperature range ?170° C. to +220° C. The principal expansion coefficients along the crystallographic axes have been determined and at room temperature (25° C.) the values ofa _a,a _b anda _c are respectively 17·7, 13·5, and 43·0, ×10^?6 (°C.)^?1. The expansion coefficients are found to vary nonlinearly, and, in particular, along thec-axis the thermal expansion shows an anomalous behaviour between ?160°C. and ?60°C. and also in the neighbourhood of +130°C. These anomalies are explained as due to homomorphous transitions in which there is a reorientation of the ?NH ₊ ³ group about the N-N axis or a re-alignment of the ?NH₂ group.     

Electrons magnetic fields and background radio emission in the galaxy

Extensive data now available on the non-thermal background radio emission from different celestial directions, and recent measurements on the energy spectrum of cosmic ray electrons in the vicinity of the earth permit one to deduce information on the mean magnetic fields and cosmic electron spectra needed to exist in different regions of the Galaxy. It is found that in order to explain quantitatively the background radio brightness distributions from the Galaxy one needs (i) the same or nearly same electron spectrum that exists in the near interstellar space, to exist in almost all regions of Galactic space, (ii) a mean magnetic field close to 6×10^?6 Gauss in the Disc in the direction of the Anti-centre, (iii) a mean magnetic field close to 2·5×10^?6 Gauss in the radio Halo and (iv) a mean magnetic field probably close to 9·5×10^?6 Gauss towards the Galactic Ridge in the direction of the Centre. Some inferences are also drawn on the confinement of cosmic rays in the Galaxy.     

The maximal Fejér operator on the spacesH p (R×···×R)

It is shown that the maximal operator of the Fejér means of a tempered distribution is bounded from thed-dimensional Hardy spaceH _p (R×···×R) toL _p (R ^d ) (1/2<p<∞) and is of weak type (H ₁ ^?i ,L ₁) (i=1,…,d), where the Hardy spaceH ₁ ^?i is defined by a hybrid maximal function. As a consequence, we obtain that the Fejér means of a functionf ∈H ₁ ^?i ?L(logL) ^d?1 converge a.e. to the function in question. Moreover, we prove that the Fejér means are uniformly bounded onH _p (R×···×R) whenever 1/2<p<∞. Thus, in casef ∈H _p (R×···×R) the Fejér means converge tof inH _p (R×···×R) norm. The same results are proved for the conjugate Fejér means, too.     

Studies in the hydrolysis of metal ions

The hydrolysis of cupric ion has been studied at various ionic strengths (0·01, 0·05, 0·1 and 0·5 M). The results are analyzed employing ‘core + links’ theory, log-log plot, normalization plot, and extrapolation method for obtaining the pure mononuclear curve. The stability constants of Cu₂(OH) ₂ ⁺⁺ , Cu₃(OH) ₄ ⁺⁺ , Cu(OH)⁺ and Cu(OH)₂ have been reported.     

Infrared spectrum of ferroelectric lithium hydrazinium sulphate [Li (N2H5) SO4]

Dielectric observations on lithium hydrazinium sulphate have shown earlier that it is ferroelectric over a range of temperatures from below ?15° C. to above 80° C. and a new type of hydrogen bond rearrangement which would allow the protons to migrate along the chain has also been suggested by others. The infrared spectrum of LiH _z S in the form of mull and as single crystal sections parallel and perpendicular to the ‘C’ axis exhibit about 21 well-defined absorption maxima. The position and the width of the maxima agree with the known structure of the crystal according to which the hydrazine group exists in the form of the hydrazinium ion, NH₂·NH ₃ ⁺ and the observed N⁺-H frequencies agree better with the new correlation curve given by R. S. Krishnan and K. Krishnan (1964). However it has been pointed out that from a comparative study of the new infrared spectra of hydrazonium sulphate and lithium ammonium sulphate that the absorption band at 969 cm.^?1 is due to N-N stretching vibration and that the fairly intense band between 2050–2170 cm.^?1 is due to the bending vibrations of the NH ₃ ⁺ group.     

The propagation in space of cosmic-ray helium nuclei and the slope of their energy spectrum

Cosmic-ray helium nuclei, along with heavier nuclei, traverse interstellar and interplanetary matter during their propagation from their “source” to the earth. Ionisation and spallation losses during this traversal modify the energy spectra with which they started. Taking these effects into account, a calculation has been made of the abundance of helium nuclei relative to that of heavier nuclei (charge Z?6) as a function of energy and the amount of matter traversed. A comparison of the results with the experimental observations suggests that the exponents of the energy spectra of the helium and heavier nuclei should differ by ～0·25 at the “source”.     

Atmospheric gamma-rays of 1–200 GeV over Hyderabad

Using a stack of hypersensitized nuclear emulsions, exposed under 10.2 g.cm^?2 of residual atmosphere over Hyderabad, India, gamma-rays of energy > 1 GeV have been studied. It is found that the observed differential energy spectrum can be best represented by two power law spectra, one for energies less than 30 GeV and the other for higher energies but with the same spectral index of 2.6; however the intensities at energies greater than 30 GeV are about three times higher than what would be expected from the extrapolation of the spectrum at lower enerjies. The implication of this observation has been examined. The neutral pion production spectrum over Hyderabad has been derived from the gamma-ray spectrum. Using this information the energy spectrum of atmospheric electrons has been deduced and a comparison made with the observed spectrum below the geomagnetic threshold energy over Hyderabad; therefrom an upper limit of 0.5 particles/(m².sr.sec.) has been deduced for the flux of re-entrant albedo electrons above 2 GeV.     

Radioactive beryllium in the atmosphere and on the earth

It is estimated that about 1,000 nuclei of radioactive Be¹⁰ (2·7 million years half-life) are produced per square meter per second by cosmic ray induced nuclear disintegrations in the atmosphere. The conditions for observing the resulting activity in rain water and in various regions on the earth are favourable and may be useful for measuring sedimentation rates and other geological surface changes during the Tertiary.     

On the regularity of oricyclic coordinates

Suppose there is defined in the plane a complete metric W^?, whose curvature K satisfies the inequality ?k ₂ ² ≤ K≤ ?k ₁ ² (k₁ and k₂ are positive constants) and some regularity hypothesis. Then in the entire domain of definition of the metric W^? one can construct regular oricyclic coordinates (x, y), in which the line element has the form ds² = dx²+ B² (x, y) · dy².