- Email: [email protected]
Lasers and resonance radiation of relativistic atoms and nuclei
Volume 44A, number 5
PHYSICS LETTERS
2 July 1973
LASERS AND RESONANCE RADIATION OF RELATIVISTIC ATOMS AND NUCLEI K.A. ISPIRIAN and A.T. MARGARIAN Yerevan Physical Institute, Yerevan, Armenia, USSR Received 18 May 1973 It is shown that due to the Doppler effect the interaction of the laser beams with relativistic beams of heavy ions results in production of resonance radiation in the vacuum ultraviolet and X-ray regions. It is proposed to use such interaction for obtaining intensive quasimonochromatic beams of gamma quanta.
The successes acthieved recently in the acceleration of heavy ions [1] permit the hope that intensive
i.e. the cross section at the resonance is approximately equal to the square of the wavelength X01 = 2ir/w01
beams of heavy relativistic atoms and nuclei will be obtained in the nearest future which can find a wide application in high energy, nuclear physics, biology etc. In this paper we consider some aspects of the interaction of such beams with intensive laser beams. Let us consider the collision of a monoenergetic beam of relativistic ions M and energy beam 2) with withmass a monochromatic E ‘yM(y = ii~/i_-j3 of laser photons with energy w 0 (71 = c = 1). In the rest system of the ions the energy of the laser photons will be w’ = w y(l ~3cos 0 ) (1)
and has a great magnitude. The part of the cross section, corresponding to the coherent scattering is determined by the same expression (2) but an other value of g [2]. In the laboratory frame the photons undergoing coherent scattering have the energy and direction of the primary photons. The ions excitedspontaneously by the other part section will radiate due of tothe thecross transi-
—
1
0
‘
where 01 is the angle between the momenta of the ions and laser photons. If the energy of the ions is such that the value of w’ approaches to the energy of one of the atomic or nuclear energy levels E1, E2 E,~ of the ions, then a resonance interaction between the laser photons and ions will take place with a total cross section ...
ir 1’nll’n 2 1 2 (2) w (w w~1) + 4”~ where ~n1 and Fn are the partial for the transition “1” “n” and total widths of the level “n”, w,~1= E~ E1 and —
-+
—
—
(2dn + 1)12(2d1 + 1). (3) Here d1 and d~are the moments of the ground “1” and the excited “n” states, respectively. At W’ = W~~1
g
—
Gres
g(~1/7r)U~~1 r~/r~)
(4)
tions from the state “n” to the ground state “1” as well as to other states, in particular to metastable states. So a possibility of selective pumping of ion 1evels with energies exceeding w0 up to 2y times arises due to the relativistic motion of the ions. In the laboratory frame the energy of the photon emitted to a transition with energy Wif by a relativistic ion will be equal to ~
(5)
W—Wf(l_13 )2/(1_13co502), 1
where 02 is the angle between ion momentum and the observation direction. In particular, when Wif = Wnl w=w0(1—~3cos01)/(1—j3cos02). (6) The photons emitted spontaneously have a certain angular and energy distribution: in the case of one level, photons with a certain energy are emitted at a given angle. Let us note, that when ‘y 1, the main part of the intensity of this incoherent radiation is emitted at small angles relative to the direction of the ions’ motion. The maximum photon energy is obtamed when 2w01 = ~ O~= 0 (f3 1) Wm~ = 47 0, (7) ~-
—~
377
Volume 44A, numberS
PHYSICS LETTERS
i.e. analogously to the Compton effect on a moving electron [3] and ondulator radiation [4], a frequency 2 times takes place due to the multiplication up to 4y Doppler effect, In the case of nonmonochromatic colliding beams the effective cross section for the interaction between the laser photons and relativistic ions, having energy distributions P(w 0) and P(E) respectively, is given by the expression
IJff=JftJ(w)P(E)P(W )dEdw e
0
(8)
. 0
Since for real beams AE/E 10-2 and Z~w/w i0~, where z~E and /~w0are the full widths at half heights of the distributions P(E) and P(w0), then AE/E and the width of the photons cxciting the ions is wider than the corresponding F,7). Therefore, according to [5] , the radiation will be mainly spontaneous with a width corresponding0eff to the width of and the P(w given level. To we radiation assume that P(E) estimate 0) have a Gaussian form around. E0 and w°0,and E0 and are chosen so that 2(E0/M)w°0= w~1.Then, according to [6] neff
~i
(r/w~1)/(~E/E0)
(9)
and one obtains the following estimates for Geff.
For
the atomic levels in the optical region X 5 2X ini0~ thecm, 2 X 102 and UeffX ~5 X cm [‘1w vacuum ultraviolet region X 10-15 10—6cm —‘7
—1 ~
‘1
.
2 X 10 and a 5 X 10 cm ‘in the X-ray reei~ — — gion X 10 2cm [‘/w~ 0eff 10 18cm2. 1 X10 ‘~10-10 and ÷10’8cm and While for the nuclear levels one may choose such transitions for which F/w~ 1is 2. As it e . 10-8 1010 and a ~ 1026 l024 cm seen neff is mainly greater than Compton scattering cross section (a 6.6 X 1025 cm2) [3]. In case of the collision of a laser pulse with a pulse of relativistic ions having ‘-‘ 1 cm2 cross section, 10—6 s length and ~~.~l022and ~_~l010particles, respectively, one obtains (interaction length ~~102 cm) lO~±106
378
2 July 1973
gamma quanta emitted due to the nuclear transitions, while the number of the quanta due to the optical and X-ray atomic transitions can exceed the number of the ions of the time interval between two consequent collisions with the same ion is larger than the relativistic lifetime of the corresponding level. Otherwise induced radiation which niay be enhanced by other methods [4,7] can occur. Let us note that if w’ is greater than the binding energy of a given shell, then ejection of electrons from .
the given shell takes place with a sufficiently large cross section [8] with a consequent characteristic radiation emission. The above considered processes may find application for obtaining intensive quasi-monochromatic beams of vacuum ultraviolet and X-ray quanta [9] and for investigating atomic and nuclear levels.
References ~ij HA. Grunder et al., I.E.E.E. Trans., N.S. 19 (1972) 212. 12] VB. Berestetski, E.M. Lifshits and L.P. Pitaevski, Relativistskaya kvantovaya teoiya, Part 1. (Publishing House “Nauka”, Moscow, 1968, in Russian). 13] F.R. Arutyunian and V.A. Tumanian Phys. Lett., 4 (1963) 176; R.H. Milburn, A.G. Phys.Oganesian, Lett. 10 (1963) 75. ]4] K.A.Ispirian, X-ray radiation of ultrarelativistic particles in magnetic ondulators and possibilities of its application, lecture delivered at VII Intern.
School on Experimental and theoretical physics, Yerevan, 1971 (to be published).
[5] W. Heitler, The quantum theory of radiation (Oxford UniPress, London, 1954). 16] versity A. Mitchell and M. Zemansky, Resonance and excited atoms (Cambridge University Press,radiation New York, 1934).
17] V.V. Okorokov et al., Zhur. Eksp. i Theor. Fiz., Pisma. 16 (1972) 588. 181 M.A. Duguay and P.M. Rentzepis, Appl. Phys. Lett. 10 (1967) 350. [9] A.G. Molchanov, Uspekhi Fiz. Nauk, 106 (1972) 165.
PHYSICS LETTERS
2 July 1973
LASERS AND RESONANCE RADIATION OF RELATIVISTIC ATOMS AND NUCLEI K.A. ISPIRIAN and A.T. MARGARIAN Yerevan Physical Institute, Yerevan, Armenia, USSR Received 18 May 1973 It is shown that due to the Doppler effect the interaction of the laser beams with relativistic beams of heavy ions results in production of resonance radiation in the vacuum ultraviolet and X-ray regions. It is proposed to use such interaction for obtaining intensive quasimonochromatic beams of gamma quanta.
The successes acthieved recently in the acceleration of heavy ions [1] permit the hope that intensive
i.e. the cross section at the resonance is approximately equal to the square of the wavelength X01 = 2ir/w01
beams of heavy relativistic atoms and nuclei will be obtained in the nearest future which can find a wide application in high energy, nuclear physics, biology etc. In this paper we consider some aspects of the interaction of such beams with intensive laser beams. Let us consider the collision of a monoenergetic beam of relativistic ions M and energy beam 2) with withmass a monochromatic E ‘yM(y = ii~/i_-j3 of laser photons with energy w 0 (71 = c = 1). In the rest system of the ions the energy of the laser photons will be w’ = w y(l ~3cos 0 ) (1)
and has a great magnitude. The part of the cross section, corresponding to the coherent scattering is determined by the same expression (2) but an other value of g [2]. In the laboratory frame the photons undergoing coherent scattering have the energy and direction of the primary photons. The ions excitedspontaneously by the other part section will radiate due of tothe thecross transi-
—
1
0
‘
where 01 is the angle between the momenta of the ions and laser photons. If the energy of the ions is such that the value of w’ approaches to the energy of one of the atomic or nuclear energy levels E1, E2 E,~ of the ions, then a resonance interaction between the laser photons and ions will take place with a total cross section ...
ir 1’nll’n 2 1 2 (2) w (w w~1) + 4”~ where ~n1 and Fn are the partial for the transition “1” “n” and total widths of the level “n”, w,~1= E~ E1 and —
-+
—
—
(2dn + 1)12(2d1 + 1). (3) Here d1 and d~are the moments of the ground “1” and the excited “n” states, respectively. At W’ = W~~1
g
—
Gres
g(~1/7r)U~~1 r~/r~)
(4)
tions from the state “n” to the ground state “1” as well as to other states, in particular to metastable states. So a possibility of selective pumping of ion 1evels with energies exceeding w0 up to 2y times arises due to the relativistic motion of the ions. In the laboratory frame the energy of the photon emitted to a transition with energy Wif by a relativistic ion will be equal to ~
(5)
W—Wf(l_13 )2/(1_13co502), 1
where 02 is the angle between ion momentum and the observation direction. In particular, when Wif = Wnl w=w0(1—~3cos01)/(1—j3cos02). (6) The photons emitted spontaneously have a certain angular and energy distribution: in the case of one level, photons with a certain energy are emitted at a given angle. Let us note, that when ‘y 1, the main part of the intensity of this incoherent radiation is emitted at small angles relative to the direction of the ions’ motion. The maximum photon energy is obtamed when 2w01 = ~ O~= 0 (f3 1) Wm~ = 47 0, (7) ~-
—~
377
Volume 44A, numberS
PHYSICS LETTERS
i.e. analogously to the Compton effect on a moving electron [3] and ondulator radiation [4], a frequency 2 times takes place due to the multiplication up to 4y Doppler effect, In the case of nonmonochromatic colliding beams the effective cross section for the interaction between the laser photons and relativistic ions, having energy distributions P(w 0) and P(E) respectively, is given by the expression
IJff=JftJ(w)P(E)P(W )dEdw e
0
(8)
. 0
Since for real beams AE/E 10-2 and Z~w/w i0~, where z~E and /~w0are the full widths at half heights of the distributions P(E) and P(w0), then AE/E and the width of the photons cxciting the ions is wider than the corresponding F,7). Therefore, according to [5] , the radiation will be mainly spontaneous with a width corresponding0eff to the width of and the P(w given level. To we radiation assume that P(E) estimate 0) have a Gaussian form around. E0 and w°0,and E0 and are chosen so that 2(E0/M)w°0= w~1.Then, according to [6] neff
~i
(r/w~1)/(~E/E0)
(9)
and one obtains the following estimates for Geff.
For
the atomic levels in the optical region X 5 2X ini0~ thecm, 2 X 102 and UeffX ~5 X cm [‘1w vacuum ultraviolet region X 10-15 10—6cm —‘7
—1 ~
‘1
.
2 X 10 and a 5 X 10 cm ‘in the X-ray reei~ — — gion X 10 2cm [‘/w~ 0eff 10 18cm2. 1 X10 ‘~10-10 and ÷10’8cm and While for the nuclear levels one may choose such transitions for which F/w~ 1is 2. As it e . 10-8 1010 and a ~ 1026 l024 cm seen neff is mainly greater than Compton scattering cross section (a 6.6 X 1025 cm2) [3]. In case of the collision of a laser pulse with a pulse of relativistic ions having ‘-‘ 1 cm2 cross section, 10—6 s length and ~~.~l022and ~_~l010particles, respectively, one obtains (interaction length ~~102 cm) lO~±106
378
2 July 1973
gamma quanta emitted due to the nuclear transitions, while the number of the quanta due to the optical and X-ray atomic transitions can exceed the number of the ions of the time interval between two consequent collisions with the same ion is larger than the relativistic lifetime of the corresponding level. Otherwise induced radiation which niay be enhanced by other methods [4,7] can occur. Let us note that if w’ is greater than the binding energy of a given shell, then ejection of electrons from .
the given shell takes place with a sufficiently large cross section [8] with a consequent characteristic radiation emission. The above considered processes may find application for obtaining intensive quasi-monochromatic beams of vacuum ultraviolet and X-ray quanta [9] and for investigating atomic and nuclear levels.
References ~ij HA. Grunder et al., I.E.E.E. Trans., N.S. 19 (1972) 212. 12] VB. Berestetski, E.M. Lifshits and L.P. Pitaevski, Relativistskaya kvantovaya teoiya, Part 1. (Publishing House “Nauka”, Moscow, 1968, in Russian). 13] F.R. Arutyunian and V.A. Tumanian Phys. Lett., 4 (1963) 176; R.H. Milburn, A.G. Phys.Oganesian, Lett. 10 (1963) 75. ]4] K.A.Ispirian, X-ray radiation of ultrarelativistic particles in magnetic ondulators and possibilities of its application, lecture delivered at VII Intern.
School on Experimental and theoretical physics, Yerevan, 1971 (to be published).
[5] W. Heitler, The quantum theory of radiation (Oxford UniPress, London, 1954). 16] versity A. Mitchell and M. Zemansky, Resonance and excited atoms (Cambridge University Press,radiation New York, 1934).
17] V.V. Okorokov et al., Zhur. Eksp. i Theor. Fiz., Pisma. 16 (1972) 588. 181 M.A. Duguay and P.M. Rentzepis, Appl. Phys. Lett. 10 (1967) 350. [9] A.G. Molchanov, Uspekhi Fiz. Nauk, 106 (1972) 165.