Reduced Intensity Total Body Irradiation + Thymoglobulin Followed by Allogeneic PBSCT

This randomized phase II trial studies how well giving low dose total-body irradiation (TBI) with anti-thymocyte globulin followed by donor peripheral blood stem cell transplant (PBSCT) works in treating patients with hematologic malignancies. Giving reduced intensity total-body irradiation and anti-thymocyte globulin before a donor peripheral blood stem cell transplant helps stop the growth of cancer cells. It may also stop the patient's immune system from rejecting the donor's stem cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving total-body irradiation together with antithymocyte globulin before transplant may stop this from happening.