Whether you are a single woman looking for a "good" man, or a married woman hoping to keep your man, the statistics are discouraging:

There are 33 million single women -- 40 percent of the female population.

*In 1983, there were only 91 divorced men for every 137 divorced women.

*For every 223 unmarried women in their forties there are 100 unmarried men in the same age group.

*In 1980, widows outnumbered widowers six to one.

*Currently, 18 to 33 percent of the 33 million single women population are involved in affairs with married men.

*Between 40 to 50 percent of married men report having had extra-marital affairs.

*Over 15 percent of husbands report having had a series of affairs.

Like it or not, those are the facts, says sociologist Laurel Richardson, who over a period of eight years talked with 1,000 single women involved with married men. From those thousand, Richardson selected a national sample of 55 single women, ages 24 to 65, for the in-depth interviews reported in her latest book, The New Other Woman (Free Press, $17.95), a disturbing and thoughtful analysis of today's single woman's search for love.

With so few single men available and so much societal and personal pressure on the single woman to "have a man," the search is not an easy one. The alternative, says Richardson, is "to turn to socially disapproved ways to achieve heterosexual couplehood. One such way is a relationship with a married man."

Richardson says the phrase "other woman" is pejorative and now wrongly defines as "different" or "outsiders" this growing type of woman. To raise that status and lessen the stigma, Richardson deliberately capitalizes and refers to those single women as the "Other Woman" -- a reclassification many married women may argue or regret. (And yet, says Richardson, with the rise in divorce, many wives of today will find themselves in the role of the Other Woman in years to come.)

"These Other Women," contends Richardson, who is 47 and married, "may be your own sister, daughter, mother, neighbor or best friend. They are living the lives, hopes and problems of Everywoman."

What makes these single women "new" is not just their overwhelming numbers, but their independent, even "cavalier" attitude. Richardson's study showed that many "new" Other Women -- who, she says, are almost equal in numbers to the traditional, more dependent Other Woman -- prefer to maintain their autonomy by discouraging any deep emotional commitment in their love affairs. Often, says Richardson, "the new Other Woman has been hurt by men -- single or ex-husbands -- so she seeks ways to protect herself from being vulnerable."

When an independent single woman purposely chooses a married man, says Richardson, "it is because she knows he is committed to his wife and family, which gives her the freedom to focus on her career, studies or other personal interests."

In fact, she adds, "if her married lover offers to leave his wife, she may say, 'if you do, I will leave you' -- because she no longer feels she is in a safe relationship."

Despite this show of independence, single women often complained to Richardson that they got involved with a married man "unintentionally" -- that they initially misinterpreted his interest as a sign of friendship or support in her career. Such naivete' or denial, says Richardson, is rampant among women in the workplace and among divorced or widowed women who are seeking solace and companionship. The traditional single woman especially denies the normal heterosexual attraction: "She needs to realize that no matter what she is doing, she is sexy to men," says Richardson.

Once the single woman -- traditional or independent -- and a married man do become lovers, the relationship at first may be caring, loving and supportive. They may share an interest in their careers, or the man may enjoy the intimacy to talk about his feelings and expectations -- something he doesn't do with his wife. As for sex, "the secrecy, privacy and time constraints . . . aphrodisiacal," writes Richardson.

Wrapped in secrecy, the affair has a "second world" atmosphere of "fantasy, and unreality." The Other Woman gathers "proof" the relationship really exists by collecting such mementos as a postcard, dried flowers, or photos, which are treasured but "never displayed on her coffee table."

According to Richardson, some Other Women get more than love and mementos. They may receive monetary or material "extras," which, she says, are difficult for the younger women to comfortably accept, but not for the growing numbers of older divorced women who are used to being supported by a man.

"These are rarely gifts of money," says Richardson, "but a women who makes under $7,000 a year gets a financial boost when her married lover takes her out to dinner at least once a week."

Does the new Other Woman feel guilt about hurting the wife?

She may feel it, says Richardson, but "contrary to societal expectations . . . contemporary women rarely express guilt over their involvements with married men. The scarlet letter has faded."

Both the single woman and her married lover can deny the wife even exists, says Richardson, explaining that such denial can stem from contemporary social mores and attitudes that allow us to view ourselves as blameless. Adding to this so-called "guiltless" behavior is the modern belief that marriage is not a permanent status. As one Other Woman in the study said: "The line between marriage and nonmarriage seems more ephemeral nowadays. Maybe, if he's married now, it doesn't mean he'll be married six months from now."

The wife too may be denying that there is someone else in her husband's life -- making it easier for the affair to survive. Or when the Other Woman and wife know each other socially or professionally -- something more common than in days past -- the single woman may compartmentalize the wife, putting her in a separate world that has nothing to do with her relationship with the man they share.

"The greater the dependence -- be it psychological, emotional or financial -- that the Other Woman has on her married lover," says Richardson, "the greater the feelings of powerlessness, and the less the perceived ability to alter one's life."

The traditionally minded Other Woman -- who was "heftily represented" in Richardson's study -- gives up her own interests and withdraws from her friends and her family. Her weekends become a waiting game "just in case he summons her." Says Richardson: "The man becomes the constant gatekeeper."

The culmination of this sacrifice comes when the affair ends -- which, according to Richardson, it invariably does. Few married men divorce and marry their Other Woman. The affair usually ends because another Other Woman is discovered, or the wife has given an ultimatum, or the man goes through a midlife change, moves away or dies. All of these reasons are traumatic, says Richardson, "leaving the single woman with no feeling of closure."

The "new," more independent Other Woman, however, "mutually winds down" the relationship and "gets on to better things," says Richardson, such as "more time for her career or even another relationship." The more dependent Other Woman is left feeling abandoned, unable to express her anger and often "still in love."

Richardson found that when the Other Woman tries to maintain a friendship with her married ex-lover ("After all, we started out as friends," the single woman reasons), it only drags on the dependency. "Because the woman defines friendship as giving and nurturing . . . she must as a friend swallow her hurt and pain, thus linking herself to him, not letting herself get rid of her anger, humiliation and shame.

"Men don't want to be friends after a sexual involvement," says Richardson. "They feel that they are over with it and don't have to maintain a friendship to justify their actions."

What then is the future for these Other Women?

The "new" Other Women will continue to be involved with married men, claims Richardson, because they need the financial "extras," or the emotional non-commitment at this time in their life. The more traditional Other Women will repeat their misery with a married man because they are ambivalent and "lack a firm sense of self."

But "many . . . strongly reject the idea of ever again being the Other Women," says Richardson. "Through their experiences with married men, they have become more identified with the wife and with women as a group," she says, adding many Other Women may go on to insist on a monogamous marriage with a man they can trust or no marriage at all.

Whichever path taken, all 55 Other Women in Richardson's study "agreed on the advice they would offer a woman considering such a liaison: 'Be Careful.' "