EXCITATION RATE COEFFICIENTS OF MOLYBDENUM ATOM AND IONS IN ASTROPHYSICAL PLASMA AS A FUNCTION OF ELECTRON TEMPERATURE

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1 EXCITATION RATE COEFFICIENTS OF MOLYBDENUM ATOM AND IONS IN ASTROPHYSICAL PLASMA AS A FUNCTION OF ELECTRON TEMPERATURE A.N. Jadhav Department of Electronics, Yeshwant Mahavidyalaya, Ned. Affiliated to Swami Raman Teerth Marathwada University, Ned. angadjadhav2007@rediffmail.com ABSTRACT: In present work Excitation rate coefficients of the states of Molybdenm ions have been obtained sing widely tilized stard formlae proposed by Breton [1] based on Bethe Born approximation. The excitation rate coefficients of Molybdenm ions in Astrophysical plasma are determined as a fnction of electron temperatre are presented graphically. From graphs it shows that, the Excitation Rate Coefficient is a very sensitive fnction of electron temperatre before it reaches its peak vale becomes very slow varying fnction of Electron Temperatre near its satration vale. KEYWORDS: Excitation Rate Coefficient, Electron Temperatre, Stepwise excitation, Electron Impact excitation, Inelastic collisions. 1. INTRODUCTION It is well known that energy states of atoms ions in the plasma are poplated by electron collisions depoplated by collisions of ions with slow electrons. Besides the collisional processes the atomic ionic states are poplated depoplated de to some radiative processes also. Electrons passing throgh the plasma transfer their energy to the plasma particles by two types of collisions, i) Elastic collisions ii) Inelastic collisions. In elastic collisions the transfer of kinetic energy of electron in to the kinetic energy of the plasma particles (atoms or ions) takes place. In this process the kinetic energy of the colliding particles is conserved. This type of collisional process is responsible to the heating of the plasma particles to some extent. In fact the second type of collision i.e. inelastic collisions are mainly responsible for the excitation of atoms ions in the plasma. Any collision in which the internal energy of excitation of a particle is changed is referred to as inelastic collision. In this type of collision the kinetic energy of electron is converted into potential energy of colliding plasma particles the plasma particles get excited. These particles in excited states either transfer their energy back to the electron or they ndergo a transition giving radiative emission. The rate of transfer of energy from the electrons to the plasma particles may be written as, de (1) N g C e N e E c N gi N e C in E j N gi N e C dex E i dt N g is nmber of gas particles. j C e is coefficient of elastic collision. E c is energy transferred in elastic collisions. j Jadhav A.N. 16

2 C in is rate coefficient of inelastic collisions. E j is energy of the j th state excited by elastic collision. C dex is de-excitation rate coefficient. E i is energy of excited particles which transfers its energy to the electrons. The sm rns over all possible energy states of the plasma particles. 2. EXCITATION PROCESSES The processes which can poplate or depoplate the states of plasma particles are listed below. i) Stepwise excitation ii) Direct excitation iii) Penning excitation iv) Dffendck excitation 2.1 ELECTRON IMPACT EXCITATION (EIE) In this case the energy from the high energy electrons is transferred to the colliding atoms or ions in the plasma. When an electron having energy more than the excitation energy of an electron rotating arond ncles of an atom / ion collides with the atom / ion may transfer its energy to the system this may reslt in excitation of the rotating electron to a higher orbit. The probability of excitation depends pon energy of exciting electron cross section of excitation at that particlar energy. The excitation rate depends pon the excitation cross section the nmber of effective collisions made by the electron. The nmber of effective collisions is fnction of electron velocity, which intern is a fnction of electron temperatre (T e ). As we know that the plasmas consists of atoms, ions electrons, there can be two types of electron impact excitation processes depending pon whether the colliding particles are atoms in grond state or ion in grond state DIRECT AND STEPWISE EXCITATION The EIE rate coefficient is expressed in terms of excitation cross section σ electron velocity V e as < σv e >. Now for the two types of electron impact excitations we can write, R= < σ s V e > (2) D = < σ d V e > (3) R is EIE rate coefficient de to stepwise excitation. D is EIE rate coefficient de to direct excitation. σ s is EIE cross section for states from grond state of ions. σ d is EIE cross section for the states from grond state of netral atom. The velocity of an electron is fnction of its energy related to its energy E by the relation, V e = (E) 1/2 (4) The nmber dn of the electrons having energy between E E+dE is given for Maxwellian distribtion by eqation, dn=n (2/ KT e ) [E /(πkt e )] 1/2 EXP(-E / KT e )de (5) Ths the rate of excitation of energy levels by stepwise direct excitation are respectively expressed as, dr = N ( 2/ KT e ) [ E /(πkt e )] 1/2 (σ s V e ) EXP(-E / KT e ) de (6) dd = N ( 2/ KT e ) [ E/(πKT e )] 1/2 (σ d V e ) EXP(-E / KT e ) de (7) The total excitation rate coefficient can be obtained by integrating above eqation within the limits from 0 to. As the excitation process does not occr if the energy of incident electron is less than the threshold energy E s, the excitation cross section is zero for energy less than E s. Therefore the lower limit of integration is taken as E s instead of zero. Jadhav A.N. 17

3 Frther it is convenient to express the electron temperatre electron energy in ev. If T e, E de are all in ev cross section vales are in cm 2, the eqation (6) eqation (7) be written as, (8) 3 1 R 3/2 se EXP E / KTe de cm sec Es Te (9) 3 1 D 3/2 de EXP E / KTe de cm sec Es Te respectively. These eqations clearly show that if the vales of the excitation cross section are known at different vales of the electron energy, the excitation rate coefficients may be obtained at different electron temperatres. 2.2 PENNING EXCITATION Excitation energy can be exchanged between netral atoms. In particlar, an excited atom can get ionized by virte of its excitation energy, if the later is larger than the reqired ionization energy. Sch a process is made more probable if the excited atom is in metastable state has ths longer lifetime in which the particle may ndergo an effective collision. When one of the colliding atoms is in metastable state the other one is in grond state, there is a probability of ionizing second atom getting excited to the excited state depending pon the energy of the metastable atom. Sch a process is referred to as penning excitation. 2.3 DUFFENDUCK EXCITATION The process in which an ion having charge z in a grond state, when collide with the other ion having charge z' in grond state, transfers its energy to the colliding partner the other ion gets ionized. This process of ionization excitation of one ion recombination of other ion is known as dffendck excitation or charge transfer. For comptation of excitation rate coefficients, we have sed the formla proposed by Breton [1] which is sefl for comptation of excitation rate coefficient of heavy atoms like iron molybdenm as a fnction of electron temperatre. The formla proposed by Breton is based on the Bethe-Born approximation for optically allowed transitions [2] which is given below. Q1.610 e 3/2 E 1/2 5 fg Jadhav A.N. 18 (10) where Q is in cm 3 sec -1, ΔE is the excitation energy in ev. Β = (ΔE / T e ) T e the electron temperatre in ev. f is the absorption oscillator strength. g is the average effective Grond factor. The expression for g which is proposed by Mewe [3] is given below. g = A+ (Bβ - Cβ 2 + D)e β E 1 (β) + Cβ. where A, B, C D are adjstable parameters. This formla may also inclde optically forbidden monopole or qadrapole transitions (for example H - like ions, the 1s ns or 1s nd transitions respectively) spin exchange transitions (for example singlettriplet transitions in He like ions ). In these cases, f in eqation (10) assmes the f vales of the allowed transitions to the level with the same principle qantm nmber. This means for example, for the transition 1s ns 1s nd in the H - like seqence the f vale of 1s np is chosen: for 1s2 1 S 1s 2s 3 S in the He like seqence, that of 1s2 1 S 1s 2p 1 P is sed. The molybdenm transition that are inclded in excitation rate coefficient comptations together with wavelengths λ, the excitation energies ΔE the f vales, we sed the vales in C. Breton et al [1]. The isoelectronic seqences transitions considered are the same as for Iron ; the wavelength λ were either taken from calclations [6] or elsewhere obtained by extrapolation. The absorption

4 oscillator strength f were taken from [4 to 7] otherwise, we sed the systematic trends of f in isoelectronic seqences [4] as a fnction of nclear charge Z n, starting from the vales for Iron. Ths for Δn = 0 transitions, we sed f ~ (f 1 /Z ) : for Δn 0 transitions f ~ (f 0 +f 1 / Z ). In this second case we have assmed that f 1 / Z < f 0 have taken for Mo the same vales as for Fe (this is jstified by the fact that, in all cases considered in [5], the variations of f between Fe Mo are smaller than 5%). The excitation rate of an energy level of an ion is given by, dn dt N N R (11) e z z N e is the electron density. N z is the fractional density of the ion of charge z R z is the electron impact excitation rate coefficient of the state of ion of charge z. The excited states in the plasma are dexcited by ratdiative transitions. Therefore we may write, dn dt N (12) where is the radiative life time of the state. When the plasma is in steady state the excitation rate of a state wold be eqal to dexcitation rate. Therefore, Rate of excitation = Rate of dexcitation. The energy states of the ions dexcite only becase of the radiative decay therefore we may write, Rate of excitation is eqal to Rate of dexcitation by radiative decay. In other words, we can write, Rate of excitation is directly proportional to Rate of photon emission. Ths, Rate of excitation is directly proportional to Intensity of Radiation. Therefore, Intensity of radiation is directly proportional Rate of photon emission Rate of excitation of the energy states. 3. RESULTS AND DISCUSSION The excitation rate coefficient is very sefl fnction in compting the contribtion fnctions of varios spectral lines. In present work, to stdy the excitation rate coefficient of different ionic species of molybdenm, we have compted excitation rate coefficients of Mo XXV throgh Mo XLII sing Bretons formla [1] as a fnction of electron temperatre. To stdy the behavior of excitation rate coefficient, We have compted excitation rate coefficient of all the molybdenm ions reslts for Mo XXV to Mo XXVIII Mo XXXV to Mo XXXVIII are displayed in figre (1) figre (2) respectively as a fnction of electron temperatre. In all figres it is observed that the general behavior of the crves is almost similar for all the molybdenm ions. From the natre of the graph, it is seen that, initially, as the electron temperatre is increased from lower vale, the excitation rate coefficient increases linearly. Bt as the electron temperatre approaches to a vale at which the excitation rate coefficient becomes maximm, the excitation rate coefficient increases non-linearly. The non linearity in the crve increases as excitation rate coefficient approaches towards satration. Frther; the electron temperatre increases, the vale of electron temperatre at which excitation rate coefficient satrates, the excitation rate coefficient decreases bt rate of decrease in excitation rate coefficient will be very slow. From all the graphs in figre (1) (2), it shows that the excitation rate coefficient (ERC) is very sensitive fnction of the electron temperatre before it reaches its peak vale bt the variation of the fnction becomes very slow varying fnction of electron temperatre near its satration vale. For example in figre 6.3, the ERC for Fe XV increases linearly pto electron temperatre 9 ev. The crve proceeds Jadhav A.N. 19

5 nonlinearity till the ERC reaches to satration. ERC reaches to satration at electron temperatre 135 ev. Fig.1 Excitation Rate Coefficient As A Fnction Of Electron Temperatre. Excitation rate coefficient (ERC) is very sensitive fnction of the electron temperatre before it reaches its peak vale bt the variation of the fnction becomes very slow varying fnction of electron temperatre near its satration vale. REFERENCES [1] C Breton, C. De Michelis M. Mattioli "Ionisation eqilibrim radiative cooling of a high temperatre plasma" J. Qantitative Spectroscopy 19, (1978), 367. [2] H.Van Regemorter, Astrophy j. 136, (1962), 906. [3] R. Mewe, Astro. Astrophy. J. 20, (1972), 215. [4] M. W. Smith W. L. Wiese, Astrophys. J. Sppl. Ser. 196, 23, (1971), 103. [5] H. C. Fawcett, N. J. Peacock R. D. Cowan, J. Phys, B1, (1968), 295. [6] M. Klapisch, R. Perell O. Weil, Rept. EUR. CEA. FC. 827, Eratom- CEA, Association, Fontenay-ax- Roses, France (1976). [7] G. A. Martin W. L. Wiese, Phys. Rev. A 13, (1976), 699. Fig. 2 Excitation Rate Coefficient As A Fnction Of Electron Temperatre. 4. CONCLUSION Jadhav A.N. 20

CONTRIBUTION FUNCTION OF MOLYBDENUM ATOM AND IONS IN ASTROPHYSICAL AND LABORATORY PLASMA AS A FUNCTION OF ELECTRON TEMPERATURE

CONTRIBUTION FUNCTION OF MOLYBDENUM ATOM AND IONS IN ASTROPHYSICAL AND LABORATORY PLASMA AS A FUNCTION OF ELECTRON TEMPERATURE COTRIBUTIO FUCTIO OF MOLYBDEUM ATOM AD IOS I ASTROPHYSICAL AD LABORATORY PLASMA AS A FUCTIO OF ELECTRO TEMPERATURE A.. Jadhav Department of Electronics, Yeshwant Mahavidyalaya, anded. Affiliated to Swami