751
ISSN 1054-660X, Laser Physics, 2007, Vol. 17, No. 5, pp. 751–754.
© MAIK “Nauka / Interperiodica” (Russia), 2007.
Original Text © Astro, Ltd., 2007.
1. INTRODUCTION
Forthcoming x-ray free electron lasers generating x
rays of high intensity open up the way for direct pho-
ton–nucleus interactions. Among them are a variety of
processes of x-ray-driven gamma emission [1]: nuclear
Stokes or anti-Stokes scattering of x-ray radiation on
isomeric nuclei, nuclear Rayleigh scattering, nuclear
resonance fluorescence. The x-ray laser radiation
allows for coherent excitation of nuclei in a controlled
manner [2], which enables one to modify or even con-
trol the nuclear excitation dynamics. Direct laser–
nucleus interactions can be used for selective pumping
of nuclear states and preparing an active medium from
the excited nuclei for the amplification of stimulated
gamma radiation.
In this paper, we consider some features of the direct
photon–nucleus interactions that are essential to under-
standing the specific types of recoil-accompanied
nuclear electromagnetic transitions. The impact of
recoil is critical to the feasibility a gamma-ray laser
with hidden inversion of nuclear state populations [3].
These features have strong effects on the reaction cross
sections of the process of interest. The situation is quite
different, therefore, from that seen with atomic transi-
tions for which recoil is typically ignored. Naturally,
the largest cross sections are obtained at the resonance
between the energy of the incident photons and the
energy of a specific nuclear transition. Thus, the types
of nuclear transitions that are of greatest interest for a
gamma-ray laser are recoil-accompanied resonance
anti-Stokes transitions with up-conversion of x-ray-
driven radiation into a flux of stimulated gamma pho-
tons. Also important is recoil-accompanied nuclear res-
onance fluorescence transitions with the emission of
stimulated gamma rays.
2. NUCLEAR ANTI-STOKES SCATTERING
WITH RECOIL
We assume a nucleus is initially in a long-lived iso-
meric state with excitation energy E
i
. Under the influ-
ence of x rays, two-photon transitions may be driven
through an intermediate level of energy E
s
to a lower
level of energy E
f
. This transition is accompanied by
absorption of an x ray of energy E
1
= ω
1
and simulta-
neous emission of a spontaneous or stimulated gamma
ray having an energy E
2
= ω
2
. The initial state of the
combined system is described by |P
0
, i, , 〉,
where P
0
is the linear momentum of the nucleus, the
isomeric state is denoted by i, is the occupation
number for incident x rays in a particular mode with
wavevector k
1
and polarization σ
1
, and is the
occupation number for the emitted gamma ray with
wave vector k
2
and polarization σ
2
. The intermediate
level is represented as two states, |P
s
, s, – 1, 〉
and |P
s
, s, , + 1〉, and the final state of the sys-
tem is represented by |P , f, – 1, + 1〉.
The probability per unit time for this transition is
given by
(1)
where L and L' are the multipolarities of the nuclear
absorption and emission transitions, respectively. The
factor ( + 1) takes into account the contributions of
either stimulated or spontaneous transitions.
The cross section for spontaneous anti-Stokes scat-
tering is determined by the expression
n
k
1
σ
1
n
k
2
σ
2
n
k
1
σ
1
n
k
2
σ
2
n
k
1
σ
1
n
k
2
σ
2
n
k
1
σ
1
n
k
2
σ
2
n
k
1
σ
1
n
k
2
σ
2
P
fi
2 ()
=
2 π
------
ω
1
c
-----
⎝ ⎠
⎛ ⎞
2 L 1 –
ω
2
c
-----
⎝ ⎠
⎛ ⎞
2 L' 1 –
M
fi
LL' , ( )
2
n
k
1
σ
1
n
k
2
σ
2
1 + ( )
× g
L
E
2
E
f
P
2
/2 M E
1
– E
i
– P
0
2
/2 M – + + ( ) ,
n
k
2
σ
2
Stimulated Gamma Emission in an Active Medium
with Hidden Inversion
A. A. Zadernovsky
MIREA Technical University, Faculty of Physics, pr. Vernadskogo 78, Moscow, 119454 Russia
e-mail: zadernovsky@mirea.ru
Received November 1, 2006
Abstract—This paper reviews some features of the nuclear electromagnetic transitions accompanied by recoil
from the momentum of absorbed or emitted photons. We have presented, based on rigorous quantum mechan-
ical calculations, the cross sections for nuclear anti-Stokes and Rayleigh scattering with recoil. The impact of
recoil is critical to the establishing the hidden inversion of nuclear state populations and amplification of stim-
ulated gamma radiation.
PACS numbers: 42.55.Vc, 23.20.Lv, 25.20.Dc
DOI: 10.1134/S1054660X07050234
QUANTUM NUCLEONICS
AND ISOMERS