Thirteen Boston area colleges and universities, including Harvard and Radcliffe, opened a center in Dorchester last week to locate and counsel college-potential students from disadvantaged back-grounds.

Financed by a $59,875 grant under the Higher Education Act of 1965, COPE will contact bright students formerly considered "severe academic risks" from slum areas in Greater Boston.

Volunteer staffs of admissions and aid officers from Boston colleges will then guide the students through the process of filing admissions papers and entering college in the fall.

"The colleges must first persuade bright youngsters in these areas they will actually admit them -- even the drop-outs," COPE's director William M. Goldsmith said Friday. "Most of them just frankly don't believe it."

Harvard and Radcliffe will send counsellors to the center at last twice a week, according to Peter K. Gunness '57, director of financial aids, who will represent Harvard on COPE's administrative committee. But Gunness does not foresee an increase in Harvard's acceptance of Boston students from the program.

"Harvard can't take many of these Boston students, convinced as we are that they are valuable to the college," Gunness said, "simply because we don't take many students from any part of the country."

Harvard's inclusion in COPE, Gunness believes, will persuade colleges in Boston to spend their scarce scholarship dollars on students "who by objective standards seem to be impossible gambles."

For several years Harvard has recruited disadvantaged students all over the country through a cooperative organization with other Ivy League colleges.

After a year's legwork Gunness and Goldsmith have signed up 13 colleges who support their plans. Gunness hopes that the number will be thirty by the end of this year, eventually including area trade schools and nursing schools.