addition of truncated normal distribution

[H. J. Wang]

Hi,

Suppose X, Y are independent random variables with normal distributions.
The means and variances are different.  Assume X1 and Y1 are random
variables with the probability distributions f(X | X>=0) and g(Y|Y>=0),
respectively. That is, X1 and Y1 the non-negative truncations of X and
Y, respectively. Does anyone know whether in this case Z = X1 + Y1 is
still a truncated normal? Any reference on this?  Thanks in advance!