The interaction in a system of two neutrons (2n) in the reaction T(d,
He-3) at energy E-d = 31 MeV is investigated experimentally. Nuclear-u
nstable (2)n, with a decay width Gamma = (1.1 +/- 0.2) MeV, is observe
d with a large transverse cross sections in the interval of angles fro
m 6 degrees to 13 degrees (d sigma/d Omega(6 degrees) similar to 10 mb
/sr in the center-of-mass system). Two wide energy peaks were observed
in the He-3 spectra. It is proposed that broad resonances with energi
es E = (3.6 +/- 0.3) and E* similar to 11.8 MeV, populated in the rea
ction T(d, He-3), are excited in the n - n system. Their energy positi
ons satisfy the interval rule E-4:E-2 congruent to 3.3, indicating the
possible existence of a ''rotational band'' with the characteristics
2(+) and 4(+). The ''radius'' of the dineutron is estimated from the r
elation Delta E = (h) over bar(2)l(l + 1)/2 mu R-2 to be similar to 8
fm. (C) 1998 American Institute of Physics. [S0021-3640(98)00511-8].